for the cupcakes
4 1/2 ounces high-quality bittersweet chocolate, finely chopped
9 tablespoons (1 stick plus 1 tablespoon) unsalted butter, room temperature
1 cup confectioners’ sugar
6 large eggs, separated, at room temperature
1 teaspoon vanilla extract
1/2 cup granulated sugar
1 cup all-purpose flour
4 tablespoons rum
for the frosting
1 cup (2 sticks) unsalted butter, softened to room temperature
1 teaspoon finely chopped lime zest
1 teaspoon lime extract
1/2 teaspoon peppermint extract
pinch of salt
4 cups confectioners sugar
4 tablespoons rum
Preheat oven to 400F. Prepare a muffin pan with liners.
In the top part of a double boiler over very hot, but not simmering, water, or in a microwave at medium power, melt the chocolate. Remove from the heat or the oven, and let stand, stirring often, until cool. Beat the butter in the bowl of a stand mixer fitted with the paddle blade on medium-high speed until smooth, about 1 minute. On low speed, beat in the confectioners’ sugar. Return the speed to medium-high and beat until light in color and texture, about 2 minutes. Beat in the egg yolks, one at a time, scraping down the sides of the bowl. Beat in the chocolate and vanilla.
Beat the egg whites and granulated sugar in a large bowl with an electric mixer on high speed just until they form soft, shiny peaks. Do not overbeat. Stir about one fourth of the beaten whites into the chocolate mixture to lighten it, then fold in the remaining whites, leaving a few visible wisps of whites. Sift half of the flour over the chocolate mixture, and fold in with a rubber spatula. Repeat with the remaining flour.
Fill the lined muffin cups three-quarters full, being careful not to overfill. Bake until a toothpick inserted in the center of the cupcake comes out clean, about 20-22 minutes. Cool the cupcakes in the pan for 5 minutes, then transfer to a wire rack to cool completely.
Once cooled, pour rum in a small bowl. Either dip or using a pastry brush, infuse a bit of rum into each cupcake. Let set while you make the frosting.
To make the frosting, place butter, lime zest and extracts in the work bowl of your stand mixer. Whip to combine. Add salt, then add the confectioners sugar. Whip until very fluffy. Add rum and whip again. You may have to add a little more confectioners’ sugar if the rum makes the frosting liquidy again. Let set in the refrigerator for 15-20 minutes.
Frost cupcakes liberally and garnish as desired. Store cooled until ready to serve.