Heat the oven to 350°F (175°C) and line a 12-cup muffin pan with paper liners.

Crush 6 Thin Mints and place about 1 teaspoon of crumbs into the bottom of each liner. Reserve the remaining cookies for the frosting or decoration.

Whisk the flour, cocoa powder, sugar, baking soda, baking powder, and salt together in a medium bowl.

In a separate bowl, whisk the room-temperature egg, buttermilk, oil, and vanilla extract until smooth.

Add the wet mixture to the dry ingredients and stir just until combined. Carefully mix in the hot coffee or hot water last; the batter will be thin, which is normal.

Divide the batter among the liners, filling each about two-thirds full. Bake for 18–22 minutes, until the tops spring back lightly and a toothpick comes out with only a few moist crumbs.

Cool the cupcakes in the pan for about 5 minutes, then transfer them to a wire rack and cool completely.

Beat the softened butter until smooth and pale, about 2–3 minutes. Gradually add the sifted powdered sugar, mixing until incorporated.

Beat in the cream, vanilla, and peppermint extract. Add green food coloring if desired, continue beating until light and fluffy, and fold in finely crushed Thin Mints if using.

Pipe or spread the frosting over the cooled cupcakes. Finish with cookie crumbs, a halved Thin Mint, or a drizzle of melted chocolate.