For the Brownie Bottom
6 ounces best-quality unsweetened chocolate
½ pound unsalted butter
1⅔ cups all-purpose flour
½ teaspoon baking powder
½ teaspoon kosher salt
4 large eggs plus 2 large egg yolks
2 cups sugar
1 tablespoon pure vanilla
For the Cheesecake Layer
1 pound cream cheese, at room temperature
1½ cups sugar
¼ teaspoon kosher salt
4 large eggs
1½ teaspoons pure vanilla extract
1 cup semisweet chocolate chips
Position a rack in the center of the oven. Preheat the oven to 325ºF. Line a 9x13-inch pan with foil. Butter the foil.
In the top of a double boiler over simmering, not boiling water, melt the chocolate and the butter, stirring to combine. Set aside to cool to warm.
In a medium bowl, whisk together the flour, baking powder, and salt.
In a large bowl, whisk together the eggs, egg yolks, sugar, and vanilla until smooth.
Pour the chocolate mixture into the egg mixture and combine with a whisk. Add the flour mixture to the chocolate/egg mixture and stir until just combined. Pour the brownie batter into the prepared pan and spread evenly.
In the bowl of an electric mixer fitted with the paddle attachment, cream together the cream cheese, sugar, and the salt until light and fluffy, about 5 minutes. Add the eggs, 2 at a time, and mix well after each addition. Scrape down the sides of the bowl. Stir in the vanilla.
Pour the cheesecake mixture over the brownie layer. Sprinkle the chocolate chips evenly over the cheesecake layer.
Bake about 1 hour and 10 minutes, or until lightly golden. Remove to a wire rack to cool. Cool completely before slicing and store in an airtight container in the refrigerator. May be served cold or at room temperature.
Store the brownies in a single layer in an airtight container in the refrigerator for up to 1 week. For longer storage, freeze in an airtight container for up to 2 weeks. Do not uncover before defrosting.