Heat oven to 350° F.
Butter an 8-inch square baking pan. Line with 2 crisscrossed pieces of parchment, buttering in between the pieces to help them stick and leaving an overhang on all sides. Butter the top of the parchment.
Whisk together the flour, cocoa, salt, and baking powder in a medium bowl; set aside.
Combine the butter and unsweetened chocolate in a large microwave-safe bowl. Microwave on high in 30-second intervals, stirring in between, until melted. Let cool slightly.
Whisk in the sugars, eggs, espresso, and vanilla until smooth. Add the flour mixture and mix until just combined. Fold in the bittersweet chocolate. Spread the batter in the prepared pan and bake until a toothpick inserted in the center comes out with a few moist crumbs attached, 35 to 40 minutes.
Let cool completely in the pan.
Holding the paper overhang, lift the brownies out of the pan and transfer to a cutting board. Cut into 16 squares. *Note: Total Time includes cooling time.