Place the cocoa powder in a medium heatproof bowl. Add the coffee, and whisk until smooth; set aside.

Place the sugar, flour, baking powder, baking soda and salt in the bowl of a stand mixer fitted with the paddle attachment, and whisk to combine. (Alternatively, use an electric hand mixer and large bowl.) Add the eggs, milk, oil and vanilla. Beat on medium speed until smooth and fluffy, about 2 minutes. Add the cocoa mixture and beat on low speed until just combined, about 1 minute more. The batter will be thin. Transfer the batter to the baking dish.

Bake for 30 minutes. Rotate the baking dish, and bake until a tester inserted in the center of the cake comes out clean, 20 to 30 minutes more. Remove the pan to a wire rack and let cool until warm to the touch, about 1 hour. Meanwhile, make the frosting.

Make the frosting: Place the cocoa powder in the bowl of a stand mixer fitted with the whisk attachment. (Alternatively, use an electric hand mixer and large bowl.) Add the butter, and whisk until dissolved. Add milk and peppermint extract. Turn the mixer to low speed, and slowly add the powdered sugar. Once incorporated, increase the speed to medium and mix until smooth and creamy.

Spread the frosting in an even layer on the cake. Sprinkle with the crushed peppermint candies.

Recipe notes: Leftovers can be wrapped in plastic wrap and stored at room temperature for up to three days.

(Kelli Foster is associate food editor for TheKitchn.com, a nationally known blog for people who love food and home cooking. Submit any comments or questions to editorial@thekitchn.com.)