Preheat the oven to 350°F (177°C). Line a 12-count muffin pan with cupcake liners. Set aside.

Melt the butter and chocolate together in the microwave. Microwave in 30 second increments, stirring between each time. You may also melt the butter and chocolate over low heat on the stovetop. Stir until combined, then mix in the instant coffee. Set aside to slightly cool.

In a medium bowl, toss the cocoa powder, flour, baking soda, baking powder, and salt together until thoroughly combined. Set aside. In a large bowl, whisk the eggs, sugar, brown sugar, vanilla extract, and peppermint extract together until smooth. Add the cooled butter/chocolate and whisk until smooth. Add half of the flour mixture, then half of the buttermilk. Repeat until everything is added. Stir until combined; do not overmix. The batter will be very thick like pudding.

Divide the batter between 12 liners in your cupcake pan. Bake for 18 minutes, or until a toothpick inserted in the center comes out clean. Allow to cool completely before frosting.

Beat softened butter on medium speed with an electric or stand mixer. Beat for about 3 minutes until smooth and creamy. Add confectioners’ sugar, heavy cream, vanilla extract, and peppermint extract with the mixer running. Increase to high speed and beat for 3 full minutes (the longer you beat, the creamier the frosting!). Add more confectioners’ sugar if frosting is too thin or more cream if frosting is too thick. Add salt if frosting is too sweet (I add about ⅛ teaspoon).

Frost cooled cupcakes. There may be leftover frosting depending how much you use on each cupcake. Drizzle with melted chocolate. Top with crushed candy canes right before serving.

Store leftovers in the refrigerator for up to 4-5 days.