Preheat oven to 350 degrees F (175 degrees C). Line an 8x13-inch or 9x13-inch baking dish with parchment paper. Spray lightly with Non-Stick Baking Spray (to taste).
Melt Butter (1 cup) in a sauce pan. Allow the butter to cool for about 15 minutes.
While the butter is cooling, using a hand held mixer, combine the Cream Cheese (8 ounce), Sour Cream (1/2 cup), Egg (1), Granulated Sugar (1/2 cup), and Vanilla Extract (1/2 teaspoon) until smooth and creamy. Set aside.
To the butter, add the Granulated Sugar (2 cup), Egg (4), and Vanilla Extract (1/2 tablespoon). Mix until combined well.
Add the All-Purpose Flour (1 1/2 cup), Unsweetened Cocoa Powder (1 cup), Baking Powder (1 teaspoon), and Salt (1/4 teaspoon). Stir well, then fold in the Semi-Sweet Chocolate Chips (2 cup).
Pour the brownie mixture into the baking dish and spread evenly. Top with the cheesecake mixture. Using a spoon, swirl the cheesecake into the brownies.
Bake for 35 to 45 minutes. If you like your brownies more fudgy, cook for 35 and a pick inserted will come out wet. If you want them more done, cook for 45 minutes or until a pick inserted comes out with crumbs.
Let the brownies cool completely in the pan. Carefully lift them out with the parchment paper. Cut into squares.