Preheat oven to 350 degrees (F). Spray an 8×8 pan with non-stick spray and then lay thick strips of parchment paper across the bottom of the pan in a cross shape. This will make it easier to lift the brownies out of the pan once cooled.
In a medium bowl mix with a hand mixer combine the melted butter and brown sugar. When fully combined add the eggs and vanilla. Beat until fully combined and light in color.
In a small bowl combine the flour, cocoa powder, and salt. Whisk to combine and remove any lumps.
Add the dry ingredients to the wet ingredients and mix until just combined. Overmixing will create tough brownies.
Fold the chocolate into the mixture and pour into the prepared baking dish.
For Cheesecake Topping:
In a medium bowl, add the softened cream cheese and sugar and whisk until smooth.
Add the egg and vanilla extract and whisk until fully combined.
Pour the cheesecake topping over the brownie batter and use a knife to swirl the two together.
Bake for 35-40 minutes or until a toothpick inserted in the center comes out with a few moist crumbs.
Remove from oven and allow to cool completely before lifting out of the pan.