Preheat oven to 325 F. Spray a 13x9-inch pan with cooking spray.
Whisk 3 eggs together in a large bowl until light and fluffy. Add 1 cup sugar and stir.
Place 8 tablespoons butter and the unsweetened chocolate in a microwave-safe bowl. Microwave until just melted. Stir into the sugar mixture. Then, fold in 1 cup flour, baking powder, salt, and 1 teaspoon vanilla.
In another large bowl, combine the cream cheese, 6 tablespoons butter, ⅓ cup sugar, 2 eggs, 2 tablespoons flour, and 1 teaspoon vanilla. Beat with an electric mixer until combined.
Pour half of the brownie mixture into the prepared pan. Top with the cream cheese mixture.
Dollop the remaining brownie mixture in tablespoon-sized pieces on top of the cream cheese mixture. Swirl with a knife.
Bake for 35 minutes and let cool.
For the frosting, combine 3 tablespoons butter, cocoa powder, powdered sugar, milk, and remaining 1 teaspoon vanilla extract. Beat on high with an electric mixer until smooth.
Frost the cooled brownies with the frosting. Cut into squares and serve.