Preheat Oven and Prepare Pan
Preheat oven to 350°F (175°C). Line an 8×8-inch baking pan with parchment paper, leaving overhang on two sides for easy removal.
Make the Brownie Batter
In a medium bowl, whisk melted butter and 1 cup sugar until well combined. Add 2 eggs and 1 tsp vanilla extract; whisk until glossy.
Sift in cocoa powder, flour, salt, and baking powder. Gently fold together just until no dry streaks remain. Set aside.
Make the Cheesecake Layer
In another bowl, beat the softened cream cheese until smooth. Add 1/4 cup sugar, 1 egg, and 1/2 tsp vanilla extract. Mix until creamy and lump-free.
Assemble the Brownies
Spread two-thirds of brownie batter evenly in prepared pan. Pour cheesecake batter over it. Drop spoonfuls of the remaining brownie batter on top and swirl gently with a knife or toothpick to create a marbled effect.
Bake
Bake for 35–40 minutes, until the center is set and a toothpick inserted comes out with moist crumbs. If using chocolate chip topping, drizzle on at minute 30 and return to oven for last 5 minutes.
Cool and Chill
Let cool completely in the pan, then refrigerate for at least 2 hours (preferably overnight) before cutting into squares.