Preheat oven to 350°F (175°C). Line a 12-cup muffin tin with paper liners.
In a large bowl, whisk flour, sugar, cocoa, baking powder, baking soda, and salt until no lumps remain.
Add buttermilk, oil, egg, vanilla, and peppermint extract.
Whisk until smooth and glossy.
Pour in the hot coffee (or water) and whisk gently until combined. The batter will be thin. Fold in mini chocolate chips if using.
Divide batter evenly among liners, filling each about two-thirds full.
Bake 16–19 minutes, or until a toothpick comes out with a few moist crumbs.
Do not overbake.
Cool in the pan 5 minutes, then transfer cupcakes to a rack to cool completely before frosting.
Make the frosting: Beat softened butter on medium-high until creamy, about 2 minutes. Add 3 cups powdered sugar, vanilla, peppermint, salt, and 2 tablespoons cream. Beat on low to combine, then on medium-high until fluffy, 2–3 minutes.
Adjust consistency with more sugar (thicker) or cream (looser). Add food coloring if desired.
Frost cooled cupcakes with a piping bag or offset spatula. Finish with mini chips, shavings, or a drizzle.