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 cool slightly.

In a large mixing bowl, combine the melted chocolate mixture with 1 cup granulated sugar and 1 cup brown sugar. Mix well. Add in 4 eggs and 1 teaspoon vanilla extract, stirring until fully incorporated.

Sift in the flour and salt, mixing until just combined. Do not overmix. Pour half of the brownie batter into the prepared baking pan and spread evenly.

In another bowl, beat together the softened cream cheese, 1/4 cup granulated sugar, 1 egg, and 1 teaspoon vanilla extract until smooth. Drop spoonfuls of the cream cheese mixture over the brownie batter in the pan. Use a knife or toothpick to swirl the cream cheese into the brownie batter.

Pour the remaining brownie batter over the cream cheese layer and spread evenly.

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