Preheat oven to 350°F. Line the bottom and side of an 8 inch by 8 inch baking pan with parchment paper. Alternatively, grease and flour the pan.

Place the butter and chocolate in a 2 quart saucepan over low heat, stirring frequently until all ingredients are fully melted. Remove from heat. Stir in the brown sugar and vanilla. Set aside.

In an electric mixer with either the paddle or whisk attachment, beat eggs on a medium speed. Once the eggs start to get foamy, increase the mixer to high and add the sugar (just the white sugar) slowly, a little bit at a time. Once all the sugar has been added, allow the eggs and sugar to continue beating for about 10 minutes until it is thick, pale yellow, and forms a ribbon when dropped on itself.

Meanwhile, in a large bowl, whisk together all of the ingredients for the peanut butter cheesecake. Set aside.

During the last minute of the eggs and sugar beating, mix in the flour and salt to the chocolate mixture, just until combined.

With a spatula, gently fold in the beaten eggs to the chocolate mixture. Fold (do not mix) the batter until fully incorporated. Pour the brownie batter into prepared pan.

Dollop the peanut butter cheesecake in 9 clumps over the brownie batter. With a metal spatula or a knife inserted half way into the batter, swirl the peanut butter cheesecake into the brownie batter. Turn the pan 90° and do another set of swirls. One or two swirls per side should suffice. Do not be tempted to over swirl. You want to do this quickly to avoid losing air bubbles in the brownie batter.

Bake for 35-40 minutes. A toothpick inserted should come out clean and there should not be any jiggling in the center of the pan. Cool completely in pan on wire rack.