Make the cake:

1. Preheat the oven to CONVECTION/BAKE 350°F. Grease a 9-by-13-inch cake pan with the softened butter and set aside.
2. In a large bowl, sift together the flour, cocoa powder, baking powder, baking soda, and salt.
3. In another large bowl, whisk together the milk, granulated sugar, brown sugar, oil, chocolate, eggs, instant espresso, and vanilla extract until smooth.
4. Pour the liquid ingredients into the dry ingredients and whisk together until completely combined.
5. Pour the batter into the prepared pan and bake until a cake tester inserted into the center comes out clean, 25 to 30 minutes.
6. Transfer the pan to a wire rack to let the cake cool.

Make the frosting:

1. In a medium bowl, sift together the confectioners’ sugar and cocoa powder.
2. Using an electric mixer, beat the butter in a large bowl on medium-high speed until light and airy, about 3 minutes.
3. Scrape down the bowl and add the sifted confectioners’ sugar and cocoa powder, the cream, vanilla extract, and salt.
4. Beat on low speed until the dry ingredients are moistened, then increase the speed to medium-high and continue to beat, scraping down the sides of the bowl as necessary, until the frosting is very airy, about 2 minutes.
5. Spread the frosting over the cooled cake. Cut into squares and serve.

Variations:

Peanut Butter–Frosted Cupcakes

Make the cake:

1. Line a 12-cup muffin tin with cupcake liners.
2. Divide the cake batter among the muffin cups and bake until the cupcakes spring back when pressed lightly and a cake tester inserted into the center of a cupcake comes out clean, 15 to 20 minutes.
3. Transfer the pan to a wire rack to let the cupcakes cool for 10 minutes, then remove them from the pan.

Make the frosting:
Substitute ⅔ cup smooth peanut butter for the cocoa powder.

Mocha-Cream Layer Cake

Make the cake:
Line the cake pan with parchment paper and then lightly grease the paper with the softened butter. Bake the cake as instructed. Let the cake cool in the pan for 30 minutes, then invert it onto a wire rack to cool completely.

Make the mocha whipped cream:

1. In a large bowl, combine 2 cups heavy cream, 1⁄2 cup unsweetened natural cocoa powder, 1⁄2 cup confectioners’ sugar, 2 tablespoons instant espresso powder, 1 teaspoon vanilla extract, and 1⁄4 teaspoon salt.
2. Using an electric mixer, beat on low speed until frothy, about 30 seconds, then gradually increase the speed to high and continue to beat until stiff peaks form, 1 1⁄2 to 2 minutes.
3. Transfer the cooled cake to a work surface so that the long side faces you.
4. With a serrated knife, cut the cake into 2 even layers.
5. > Place 1 cake layer on a rimless platter or cake plate. To keep the platter (or plate) neat while you frost the cake, place 4 strips of waxed or parchment paper under the 4 sides of the cake.
6. Spread 1 1⁄2 cups of the mocha whipped cream on top of the cake layer, then place the second cake layer gently on top.
7. Spread the top and sides of the cake with the remaining mocha whipped cream.
8. Remove the waxed paper strips, cut into wedges, and serve.

Natural Cocoa Powder vs. Dutch-Processed Cocoa

For this cake, be sure to buy natural cocoa powder instead of Dutch-processed. Dutch-processed cocoa has a darker color and a richer, less acidic taste. It reacts with baking powder and baking soda differently than natural cocoa powder, so the cocoa powders are not interchangeable in recipes that rely on these leaveners.