Preheat the oven to 350°F (175°C). Line a 13 x 9 x 2-inch baking dish with parchment paper (leave a slight overhang for easy removal) and set aside.
In a medium mixing bowl combine 1 cup melted butter, 1 cup granulated sugar, and 1 cup brown sugar. Stir or beat until combined.
Add the 4 large eggs, one at a time, mixing after each addition. Add 1 teaspoon vanilla extract and mix until smooth.
In a separate bowl whisk together 2 cups all-purpose flour, 1/3 cup unsweetened cocoa powder, 1 teaspoon baking powder, and 1/2 teaspoon salt.
Gradually add the dry ingredients to the wet ingredients, mixing until just combined and no large streaks of flour remain. Scrape the sides and bottom of the bowl as needed.
Spread the brownie batter evenly into the prepared baking dish and smooth the top with a spatula.
Bake for 30–35 minutes, or until a toothpick inserted into the center comes out clean. Remove from the oven and place the pan on a wire rack to cool completely in the pan.
While the brownies cool, make the cookie-dough frosting: in a medium bowl combine 1/2 cup softened butter and 3/4 cup brown sugar. Beat with a hand mixer until smooth and lighter in color.
Add 1 teaspoon vanilla extract and mix to combine.
Add 1 1/4 cups all-purpose flour and 1/2 teaspoon salt. Mix on low speed until the flour is incorporated and the mixture is crumbly.
Pour in 5 tablespoons milk and beat until the mixture becomes thick and fluffy and reaches a spreadable consistency.
Stir in 1 cup mini chocolate chips until evenly distributed.
Once the brownies are completely cool, spread the cookie-dough frosting evenly over the top. Use the parchment overhang to lift the brownies from the pan before cutting, if desired.