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

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

In a large mixing bowl, combine the granulated sugar, brown sugar, and eggs. Whisk until well combined. Stir in the melted chocolate mixture and vanilla extract.

Add the flour and salt to the chocolate mixture, stirring until just combined. Do not overmix.

In a separate bowl, beat the softened cream cheese with 1/4 cup granulated sugar, 1 egg, and 1 teaspoon vanilla extract until smooth and creamy.

Pour half of the brownie batter into the prepared baking pan, spreading it evenly. Spoon dollops of the cream cheese mixture over the brownie layer, then pour the remaining brownie batter on top. Use a knife or skewer to swirl the cream cheese mixture into the brownie batter for a marbled effect.

Bake in the preheated oven for 30-35 minutes, or until a toothpick inserted into the center comes out with a few moist crumbs. Allow to cool in the pan for at least 30 minutes before cutting into squares.