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. 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, 14 to 15 minutes, rotating sheets halfway through. Transfer cookies to a wire rack to cool completely.