Make the brownie batter first: In a microwave safe bowl, melt the butter and baking chocolate in 20 second increments. Stir well after each. Set aside and let cool.
Whisk the sugar into the chocolate/butter mixture. Add the eggs one at a time, mixing well after each addition. Whisk in the vanilla. With a wooden spoon or spatula, gently fold in the flour, cocoa powder and salt. Set aside.
Preheat oven to 350°F. Line a 9x9 baking pan with parchment or foil. Leave some overhang so you can easily lift brownies out of the pan.
Make the Peanut Butter Cheesecake batter: In the bowl of a stand mixer, using the paddle attachment, beat the cream cheese for one minute until smooth. Add the peanut butter and mix until fully incorporated and smooth. Be sure to break up any chunks of cream cheese that may be hiding in there. Add the sugar, egg, flour and vanilla. Mix until well combined.
Assemble the layers: Spread 2/3 of the brownie mixture into the prepared baking pan. Be sure to spread the batter to all the edges and fill the corners. Carefully spread all of the peanut butter cream cheese mixture on top of the brownie layer. Top it with the remaining brownie batter and spread evenly to cover the top. Sprinkle the chocolate chips on top. *Optional: Using a knife, you can make some swirls, slightly mixing the batters together-leave this option out if you want more defined layers.
Bake for 37-40 minutes or until a toothpick inserted comes out mostly clean with only a few moist crumbs. The edges of the brownies will start to pull away from the pan.
Cool the brownies in the pan, sitting on a wire cooling rack for 40 minutes. Place pan in refrigerator for 2 hours to allow the cheesecake layer to set. It should be cold before slicing.
Once the brownies have chilled, lift them out of the pan and slice. Makes 16 brownies. *I like to store them in the refrigerator - they taste so good cold! However, you can keep them in an airtight container, at room temperature for a day.