Preheat oven to 350º F. Line cookie sheets with parchment paper or a nonstick baking mat.
Cream together butter and granulated sugar until light and fluffy, about 3 minutes. Add egg and mix until well-combined. Stir in flour, cocoa powder, baking powder, salt, espresso powder and vanilla.
Scoop cookie dough by the tablespoon full and roll into a ball.
Place cookie dough onto baking sheet, spacing about 1 1/2-inches to 2 inches apart. Lightly press each cookie down. Bake for 8 to 10 minutes. Remove from oven and cool.
Peppermint Bark Topping:
Melt white chocolate chips in a microwave safe bowl according to package instructions. Remove from microwave and stir in peppermint extract. Spoon onto top of cookie and top with sprinkle of crushed peppermint candy per cookie.