For brownie batter
1 stick (1/2 cup) unsalted butter, cut into pieces
2 ounce unsweetened chocolate, chopped
1 cup sugar
2 large eggs
1/2 teaspoon pure vanilla extract
2/3 cup all-purpose flour
For cheesecake batter
8 ounces cream cheese, well softened
1/3 cup sugar
1 large egg yolk
1/4 teaspoon pure vanilla extract
Make brownie batter:
Put oven rack in middle position and preheat oven to 350°F. Butter an 8-inch square baking pan.
Heat butter and chocolate in a 3-quart heavy saucepan over moderately low heat, whisking occasionally, just until melted. Remove from heat and whisk in sugar, eggs, vanilla, and a pinch of salt until well combined. Whisk in flour until just combined and spread in baking pan.
Make cheesecake batter and bake brownies:
Whisk together cheesecake batter ingredients in a small bowl until smooth. Dollop over brownie batter, then swirl in with a knife or spatula.
Bake until edges are slightly puffed and center is just set, about 35 minutes.
Serve warm or at room temperature.