Preheat the oven to 350 degrees F (175 degrees C).
Combine 2/3 cup flour, cocoa powder, 1/4 teaspoon salt, and 1/4 teaspoon baking powder in a large bowl.
Stir 3/4 cup sugar, coffee liqueur, 2 eggs, and 1 teaspoon vanilla extract together in a large bowl. Add melted butter and the flour mixture; stir and spread batter into an ungreased 9x13-inch baking pan.
Sift 1 1/3 cups flour, baking soda, 1/2 teaspoon baking powder, and 1/4 teaspoon salt together in a large bowl.
Beat peanut butter, unsalted butter, brown sugar, and 1/2 cup white sugar together in another large bowl using an electric mixer. Stir in 1 egg and 1 teaspoon vanilla extract. Place cookie dough on top of the brownie mixture in the baking pan.
Bake in the preheated oven until cookie layer is golden brown, 18 to 20 minutes. Let cool for 15 minutes. Cut into squares and leave in the pan until fully cool, about 20 minutes more.
Place white chocolate in a microwave-safe bowl. Heat in microwave until melted, about 30 seconds. Place melted chocolate in a resealable plastic sandwich bag and cut a very tiny hole in a corner. Drizzle white chocolate over cooled cookie brownies.
The first time I tried this recipe, I placed the white chocolate topping on top and refrigerated it without cutting the bars first. I recommend cutting the bars first, otherwise the white chocolate top will get loose and come off when cutting the bars. Enjoy!