Prep the pan and oven: Heat oven to 350°F (175°C). Line a 12-cup muffin tin with paper liners.
Whisk dry ingredients: In a large bowl, whisk flour, sugar, cocoa, baking powder, baking soda, and salt until evenly combined.
Mix wet ingredients (except coffee): In a second bowl, whisk buttermilk, oil, eggs, vanilla, and peppermint extract.
Combine: Pour wet ingredients into dry and whisk until mostly smooth. Do not overmix.
Add hot coffee: Slowly whisk in the hot coffee.
The batter will be thin—this is good for a moist cupcake.
Fill and bake: Divide batter evenly among liners, filling each about 2/3 full. Bake 18–21 minutes, or until a toothpick comes out with a few moist crumbs.
Cool: Let cupcakes cool in the pan 5 minutes, then move to a wire rack to cool completely before frosting.
Make the frosting: Beat softened butter until creamy, 2 minutes. Gradually add powdered sugar, then peppermint, vanilla, salt, and enough cream to reach a smooth, fluffy consistency.
Adjust flavor: Taste and add a drop more peppermint if needed.
A little goes a long way.
Frost and decorate: Pipe or spread frosting on cooled cupcakes. Top with crushed candy canes, chocolate shavings, or a chocolate drizzle.