Measure and sift the flour, cocoa, espresso powder, baking powder, and salt as you add them into the bowl. Lightly stir to mix.
Place softened butter in a large mixing bowl. Beat with a mixer at medium speed for 1 minute. Add granulated and brown sugars, beating until well blended.
Fold the flour mixture into the sugar mixture. Finely chop the chocolate into tiny slivers and fold it into the mixture.
Divide the batter evenly into eight ramekins. Place ramekins on a jelly pan. Cover and refrigerate for four hours. **Can be made ahead and refrigerated up to 2 days.
Preheat oven to 350 degrees.
Take ramekins out of the fridge and let stand at room temperature for about 10 minutes. Uncover and bake for 20 minutes or until cakes are puffy and slightly crusty on top.
Sprinkle evenly with powdered sugar. Serve immediately.