Preheat your oven to 350°F. Grease a 9x13 inch baking pan or line it with parchment paper.

Melt the unsalted butter and chopped semi-sweet chocolate in a medium saucepan over low heat. Stir until smooth and let cool slightly.

In a large mixing bowl, combine granulated sugar, brown sugar, and the melted chocolate mixture. Stir well. Add in 4 large eggs and 1 teaspoon of vanilla extract. Mix until fully combined. Add all-purpose flour and salt, stirring gently until just combined.

In a separate bowl, beat the softened cream cheese with powdered sugar until smooth. Add 1 large egg and 1 teaspoon of vanilla extract. Mix until well blended.

Pour half of the brownie batter into the prepared baking pan. Spoon the cheesecake mixture over the brownie layer. Dollop the remaining brownie batter on top and swirl the two batters together.

Bake for 30-35 minutes. A toothpick inserted into the center should come out with a few moist crumbs.

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