Preheat your oven to 350°F (175°C). Grease a 9x9-inch baking pan with a little unsalted butter.
In a double boiler or microwave, combine the unsweetened chocolate and unsalted butter. Heat until melted and smooth, then set aside to cool.
In a large mixing bowl, combine the granulated sugar, eggs, vanilla extract, and salt. Whisk together until well combined. Gradually stir in the melted chocolate mixture until smooth. Then, fold in the flour and baking powder until just combined.
In another bowl, beat the softened cream cheese with sugar and the egg yolk until smooth and creamy.
Pour about two-thirds of the brownie batter into the baking pan. Dollop the cheesecake mixture over the brownie layer and swirl gently. Pour the remaining brownie batter on top and swirl again.
Bake for 25-30 minutes, or until a toothpick comes out with a few moist crumbs.
Let the brownies cool in the pan for at least 30 minutes before cutting into squares and serving.
