Preparation

Make the filling

• In a large, heavy saucepan, combine the rhubarb, strawberries, sugar, tapioca, and lemon juice; stir well and let stand for 15 minutes to soften the tapioca. Place the saucepan over medium heat and bring to a simmer, stirring often, until the mixture begins to thicken, about 5 minutes.
• Reduce the heat to low and cook, stirring occasionally, until the mixture is jamlike and has reduced to about 1-3/4 cups, about 35 minutes. Transfer to a bowl, let cool, cover, and then refrigerate until cold.

Make the cake layers

• Position a rack in the center of the oven and heat to 350°F. Generously butter two 8-inch round cake pans, line with parchment, and then butter the parchment.
• In a large bowl, whisk the flour, baking powder, and a pinch of salt.
• In the bowl of a stand mixer fitted with the whisk attachment, cream the butter and 1/2 cup of the sugar at high speed until light in color and texture, about 5 minutes, scraping down the bowl occasionally. Add the egg yolks one at a time, and beat at medium speed to incorporate; scrape down the bowl and then beat at high speed for 2 minutes, until the mixture is bright yellow. In a small bowl, stir together the vanilla and milk. Sift half of the flour mixture over the creamed butter; beat just until incorporated. Pour in the milk mixture; mix at low speed until just blended. Sift the remaining flour mixture on top and then beat just until incorporated.
• Divide the batter between the two cake pans, smoothing the tops evenly.
• In a clean stand-mixer bowl with a clean whisk attachment, beat the egg whites at medium speed until frothy, about 2 minutes. Gradually sprinkle in the remaining 3/4 cup sugar, scraping down the bowl as needed. Once all the sugar is added, beat the whites at high speed until glossy, medium peaks form, about 6 minutes.
• Divide the meringue between the cake pans and spread with the back of a spoon, covering most of the batter but leaving 1/2 inch from the edge of the pan uncovered; do not smooth the tops. Sprinkle the almonds over the meringue, and then bake until puffed and lightly browned, about 25 minutes. Let the layers cool in their pans on a rack; the tops will sink considerably.
• While the cake is still warm, run a knife or small offset spatula around the sides of the cake layers to loosen them from the pans. After the layers are cool, carefully invert the less attractive layer onto a baking sheet and remove the parchment. Invert onto a serving platter, meringue side up. Gently spread the rhubarb filling over the top, and then cover with the other cake layer, meringue side up. (The cake may be assembled to this point a day ahead; cover loosely with plastic wrap and refrigerate.)
• To serve, top with fresh strawberries, if you like, and slice gently with a serrated knife.