Cream together butter, brown sugar, and raw sugar with an electric mixer on medium speed until fluffy, 2-3 minutes. Add egg and vanilla, and mix on low until well combined.
Add flours, baking soda, baking powder, salt, espresso powder, and cocoa powder, and mix on low until dry ingredients are completely incorporated. Stir in chocolate pieces on lowest speed until just mixed in.
Use a medium cookie scoop or a 1 tbsp. measuring spoon to dish cookie dough onto baking sheets lined with a silicone mat or parchment paper, spacing cookies 2″ apart.
Bake cookies in preheated oven for 12-15 minutes, Allow cookies to cool on the pan for a few minutes, then transfer to a wire rack to cool completely.
Adapted from Chocolate Chip Espresso Cookies at Desserts Required.