Preparation

Make the cookies:

• Sift the flour and cocoa together into a medium bowl. With a hand mixer or a stand mixer fitted with the paddle attachment, cream the butter and sugar on medium speed until light and fluffy, about 2 minutes. Add the vanilla and salt; continue beating until blended and smooth, about 1 minute more. Add the flour-cocoa mixture and mix on low speed until a soft dough forms, about 1 minute. Chill the dough in the refrigerator until firm enough to roll into balls, 40 to 60 minutes.

  Position a rack in the center of the oven and heat the oven to 350°F. Line two cookie sheets with parchment or nonstick baking liners.

  Using your palms, roll heaping teaspoonfuls of the dough into 1-inch balls. Arrange them 2 inches apart on the lined sheets. With a lightly floured thumb or index fingertip, press straight down into the middle of each ball almost to the cookie sheet to make a deep well. (Or use the end of a thick-handled wooden spoon.)

  Bake one sheet at a time until the tops of the cookies look dry, 8 to 9 minutes. Gently redefine the indentations with the end of a wooden spoon. Let the cookies cool on the sheet for 5 minutes and then let them cool completely on racks.

Make the filling:

• Put the chocolate and butter in a heatproof bowl set in a wide skillet of almost simmering water. Stir with a heatproof spatula until almost melted, 2 to 4 minutes. Remove the bowl from the heat and stir until melted and smooth, about 30 seconds more. Stir in the mint extract. Let the filling cool, stirring occasionally, until slightly thickened and a bit warmer than room temperature, 30 to 40 minutes. Spoon the filling into a small pastry bag with a small plain tip. (Or use a small plastic bag and cut a tiny bit off a bottom corner of the bag.) Pipe the filling into the center of each cookie. Cool completely before serving or storing. The cookies will keep in an airtight container at room temperature for 4 to 5 days.