Prepare Your Pan: Preheat your oven to 350°F (175°C) and lightly grease a 9x9 inch baking pan.
Mix Brownie Wet Ingredients: In a mixing bowl, combine the melted butter, packed brown sugar, and cocoa powder. Stir well. Add the eggs, one at a time, mixing thoroughly after each. Stir in the vanilla extract until just combined.
Add Dry to Brownie Wet: In a separate bowl, whisk together the flour, salt, and baking powder. Gently fold these dry ingredients into the butter mixture until just blended. Spread this brownie batter evenly into your prepared baking pan and set aside.
Create Cheesecake Swirl: In a food processor, blend the very soft cream cheese, egg, granulated sugar, vanilla extract, and salt until the mixture is completely smooth. Pour in both the melted unsweetened and semisweet chocolates, then process again until everything is perfectly combined.
Layer and Swirl: Carefully spoon the creamy cheesecake mixture over the brownie layer in the pan, spreading it out evenly.
Bake to Perfection: Place the pan in your preheated oven and bake for approximately 40-45 minutes. To check for doneness, a toothpick inserted should come out with only a few moist crumbs.
Cool Completely: Allow your delicious brownies to cool completely before slicing into squares. For the best texture, chill them in the refrigerator before cutting. Store any leftovers in an airtight container, preferably in the fridge. Enjoy them cold or at room temperature!