In a medium bowl, sift together the all-purpose flour, baking powder, instant espresso powder, salt, and unsweetened cocoa powder. Set aside.
In a large mixing bowl, use an electric mixer to beat the unsalted butter and light brown sugar until fluffy and pale, about 3-4 minutes.
Add the eggs one at a time, beating well after each addition; eggs should be at room temperature.
Gradually add the sifted dry ingredients to the wet ingredients, mixing just until combined; do not overmix.
Cover the dough and chill it in the refrigerator for at least 30 minutes.
Preheat oven to 350°F (175°C). Scoop about 1 tablespoon of dough, flatten slightly, place a Reese's Peanut Butter Cup in the center, then fold dough around it, sealing completely. Roll dough ball in sifted confectioners’ sugar and place on parchment-lined baking sheet 2 inches apart.
Bake for 10-12 minutes until edges are set but centers are still slightly soft. Remove from oven and let rest 5 minutes on baking sheet.
Transfer cookies to a cooling rack and allow to cool completely before serving.