Preheat the oven to 350°F (175°C). Grease an 8×8-inch baking pan and line it with parchment paper, ensuring that the parchment slightly overhangs the edges to make it easier to lift out the finished bars. A well-lined pan helps the layers stay clean and distinct when removed.
In a medium mixing bowl, whisk together the melted butter and granulated sugar until the mixture looks glossy and well blended. Add the eggs and vanilla extract, stirring just until everything is fully incorporated. Avoid overmixing so the brownies stay tender instead of becoming dense.
Sprinkle in the cocoa powder, flour, salt, and baking powder. Fold the dry ingredients gently into the wet mixture until no streaks remain. The batter will be thick and smooth. Spread it evenly into the prepared pan, pressing it into the corners to create a level brownie layer that bakes uniformly.
Prepare the cheesecake layer
In a separate bowl, beat the softened cream cheese until completely smooth and free of lumps. Add the granulated sugar, mixing until the texture is creamy and consistent. The smoother the cream cheese mixture, the cleaner and more defined the layers will appear after baking.
Add the eggs one at a time, beating gently after each addition to maintain a silky texture without incorporating too much air. Mix in the vanilla extract. Pour the cheesecake batter over the brownie base and spread it evenly with a spatula, ensuring full coverage and a flat surface for even baking.
Bake for 40–45 minutes, or until the center of the cheesecake layer is just set. The middle should no longer jiggle loosely, though a slight wobble is fine and prevents overbaking. Allow the pan to cool completely at room temperature; this helps the cheesecake firm up gradually without cracking.
