Preparation

Make the cake:

• Position a rack in the middle of the oven and heat the oven to 350°F. In a double boiler, melt the chocolate with the warm water. Let cool to room temperature.
• Grease the bottom of an 18×13-inch rimmed baking sheet (a standard half sheet pan) with the softened butter. Line the pan with parchment; butter and then flour the parchment.
• With an electric mixer, whip the egg yolks in a large bowl on medium-high speed until light in color and beginning to thicken, 2 to 3 minutes in a stand mixer, or 3 to 5 min. with a hand mixer. Add 1/2 cup of the sugar and whip until very thick and pale yellow, about 2 min. Reduce the speed to low and mix in the melted chocolate. With a rubber spatula, stir in the cocoa and salt until blended.
• In a clean, dry bowl with clean, dry beaters (any grease will keep the whites from whipping), whip the egg whites with an electric mixer at medium speed until they’re frothy and begin to increase in volume, about 30 seconds. In a steady stream, add the remaining 1/2 cup sugar. Increase the speed to medium high and whip until soft peaks form, 2 to 3 min. in a stand mixer, or 4 to 6 min. with a hand mixer.
• With a rubber spatula, fold the whites into the chocolate mixture in two equal additions. You can fold in the first half vigorously to lighten the yolks, but fold in the second half gently, mixing just until the batter is evenly colored with no streaks of white. Don’t overmix. Scrape the batter into the baking pan, gently spreading and smoothing it to make sure it’s level. Bake until the top springs back lightly when touched, 22 to 25 min.

  

• Meanwhile, spread a clean dishtowel (at least as big as the cake pan) on the counter. Using a sieve, dust the towel with cocoa powder, completely covering it (this will keep the cake from sticking to the towel as it cools).

Roll the cake and let it cool:

• Immediately after taking the cake from the oven, run a small knife around the inside edge to loosen it from the pan. Invert the cake pan onto the towel in one quick motion. Remove the pan. Carefully peel off the parchment. Using both hands and starting from one of the short ends, roll up the cake and the towel together. Let cool to room temperature.

  

Make the filling and sauce:

• Put the thawed raspberries in a food processor and process until completely puréed. Pass the purée through a fine sieve to strain out the seeds. You should have about 1 cup of purée.
• Fill a wide pot or straight-sided skillet with 1 to 2 inches of very hot water. In the bowl of an electric mixer, whisk the egg whites, 1/2 cup of the sugar sugar and a generous pinch of salt until blended. Set the bowl in the pot of hot water; make sure the water comes up to at least the level of the mixture in the bowl. Whisk until the mixture is almost hot (about 120°F), about 90 seconds. Take the bowl out of the water. With an electric mixer on medium-high speed, whipe the whites until cool and thick, 2 to 3 min. Reduce to medium speed, add the butter, 1 Tbs. at a time, and mix until the butter is completely incorporated. The filling should be soft and loose; it will firm up as it chills. (If it seems very runny, refrigerate it for up to 20 min.) With the mixer on low speed, blend in 2 Tbs. of the raspberry purée and the liqueur. Set the filling aside.
• 让酱汁搅拌在一起remaining raspberry purée, the remaining 2 Tbs. sugar, the lemon juice and a pinch of salt. Add more sugar or lemon juice to taste.

Fill and roll the roulade:

• Carefully unroll the cooled, towel-wrapped cake. Spread the filling over the cake, covering it evenly to within 2 inches of the edges. Reroll the cake, without the towel this time. The filling may squish out of the ends a bit; this is fine. Line a rimmed baking sheet with foil and set a wire rack on the foil. Slide two large metal spatulas (or a spatula and your hand) under the roulade and transfer it to the rack. (Or, if working ahead, transfer it to a large sheet of plastic, wrap it snugly, and refrigerate for up to a day; transfer to the rack before glazing.)
  

Glaze the roulade:

• In a large saucepan, combine the cream, sugar, 1/2 cup of the water, and the cocoa. Bring the mixture to a boil and then reduce the heat to a simmer, whisking often, until very thick, like hot fudge sauce, 8 to 10 minutes from when the mixture began simmering. Pay close attention: This mixture boils over easily. Remove the pan from the heat. While the mixture is cooling,bloom the gelatinin the remaining 1-1/2 Tbs. of water. Melt the bloomed gelatin over very hot water or in the microwave. Whisk the gelatin into the chocolate mixture and strain the glaze through a medium sieve into a metal bowl. Let the glaze cool at room temperature until thick but still pourable, about 5 to 10 min.; the glaze should be about 110° to 120°F. (If you’ve made the cake ahead, unwrap it and put it on a rack set over a foil-lined baking sheet.)
• Pour the glaze over the roulade, using an offset spatula to help the glaze cover the top and sides evenly. Don’t worry about covering the ends; they’ll be trimmed later. Refrigerate uncovered for at least 30 min. or up to 4 hours.
  

Garnish and serve:

• With a whisk or hand mixer, whip together the cream, sugar, and vanilla until soft peaks form.
• The glaze will have “glued” the roulade to the rack, so slide a metal spatula between it and the rack to release it. Transfer the roulade to a serving platter, using two large offset spatulas to get underneath and pressing the spatulas against the rack as you go. Trim the ends of the roulade. Fill a tall container with hot water and have a dishtowel handy so that you can clean and dry the knife after cutting each slice. Using a long, sharp knife, cut 3/4-inch straight slices, or cut pieces on an angle, rinsing and drying the knife after each slice. Garnish with a small pool of raspberry sauce and a dollop of whipped cream next to each slice.
  

Make Ahead Tips

You can make the cake and filling and assemble the roulade (without the glaze) a day ahead. Wrap the unglazed roulade with plastic, refrigerate it, and glaze it the next day. You can prepare the garnishes ahead, too, but whip the cream close to serving time.

Mocha:Substitute 1 Tbs. intant espresso powder and 2 oz. bittersweet chocolate, melted and cooled to room temperature, for the raspberry purée and liqueur in the filling recipe. Omit the sugar and lemon juice used for the raspberry sauce. Garnish with the sweetened whipped cream and 36 chocolate-covered espresso beans.

或ange-Vanilla:Substitute the scraped seeds of 1 vanilla bean, 1/2 tsp. pure vanilla extract, and the finely grated zest of 1 orange for the raspberry purée and liqueur in the filling recipe. Omit the sugar and lemon juice used for the raspberry sauce. Garnish with 1/2 cup candied orange zest.

Chocolate-Peppermint:Substitute 1/2 tsp. pure peppermint extract for the raspberry purée and liqueur in the filling recipe. Add two to three drops of red food coloring to the filling if you like. Omit the sugar and lemon juice used for the raspberry sauce. Garnish with each slice with fresh mint sprigs or with crushed candy canes or peppermint candies.