Adjust oven rack to lower-middle position and preheat oven to 325 degrees.
Whisk flour, salt and baking powder in a small bowl; set aside. Spray an 8-inch baking pan with cooking spray. Fit a sheet of foil in pan and up two sides, so you can use it as a handle to pull cooked brownies from pan. Spray sheet with cooking spray.
Melt chocolates and butter in a medium bowl over a pan of simmering water or use a double broiler. Remove from heat; whisk in sugar and vanilla. Whisk in eggs, one at a time. Continue to whisk until mixture is completely smooth and glossy. Add dry ingredients, whisk until just incorporated.
Pour batter into prepared pan; bake until a toothpick or cake tester inserted in center comes out with wet crumbs, 35-45 minutes.
Cool brownies in pan on a wire rack for five minutes. Use handles to pull brownies from pan. Completely cool brownies on rack.
Once brownies are cool evenly spread cookie dough over top. I used a spatula for this. Wet fingers might also work well. Chill for 30 minutes to harden slightly. This makes it easier to cut. Serve.