Preheat the oven to 350°F (175°C). Grease a 9x13-inch baking pan or line it with parchment paper.

In a medium saucepan over low heat, melt the butter and chopped chocolate together, stirring until smooth. Remove from heat and let it cool slightly.

In a large mixing bowl, combine the granulated sugar, brown sugar, and the slightly cooled chocolate mixture. Mix well. Add the eggs one at a time, mixing well after each addition. Stir in the vanilla extract.

In a separate bowl, whisk together the flour, salt, and baking powder. Gradually add the dry ingredients to the chocolate mixture, stirring until just combined.

Pour half of the brownie batter into the prepared pan, spreading it evenly.

In another bowl, beat the softened cream cheese with the granulated sugar until smooth. Add the egg and vanilla extract, mixing until well combined. Spread the cheesecake mixture over the brownie layer in the pan.

Top with the remaining brownie batter, spreading it gently over the cheesecake layer.

Bake in the preheated oven for 30-35 minutes, or until a toothpick inserted in the center comes out with a few moist crumbs.

Allow the brownies to cool in the pan for at least 30 minutes before cutting into squares.