Preheat oven to 350 degrees, with racks in upper and lower thirds. In a medium bowl, whisk together flour, cocoa, baking powder, and salt; set aside.
Using an electric mixer, beat butter and sugar until light and fluffy. Add eggs, one at a time, beating well after each addition; mix in vanilla and peppermint extract. Combine espresso powder and melted chocolate; beat into butter mixture. With mixer on low, gradually add flour mixture; mix just until combined. Fold in chopped chocolate.
Drop dough by two heaping tablespoons, 3 inches apart, onto two baking sheets. Bake until edges are dry, 12-14 minutes, rotating sheets halfway through. Transfer cookies to a wire rack to cool completely.