Preheat oven to 350°F. Line an 8x8 inch square baking pan with parchment paper and spray with non-stick cooking spray. Set aside.
In a medium saucepan over low heat, melt the butter and chopped chocolate. Stir often until the butter and chocolate are smooth and fully melted.
Remove saucepan from the heat and set aside to cool. Then whisk in the eggs until fully combined. Whisk in the sugars, espresso powder, and vanilla extract. Set aside.
In a large bowl, whisk the flour, cocoa powder, baking powder, and salt together until combined.
Fold the wet ingredients into the dry ingredients, and gently mix with a spatula. Do not overmix (a few streaks of flour and cocoa powder are fine).
Gently fold in the chocolate chips or chunks. Pour brownie batter into prepared pan and spread evenly with a spatula.
Bake for 35-40 minutes, or until a toothpick inserted in the center comes out with a few moist crumbs. Let brownies cool on a wire rack before slicing and serving.