CHOCOLATE CHEESECAKE:
5 ounces bittersweet chocolate (70% cocoa), chopped
Two 8-ounce packages cream cheese, at room temperature
1/2 cup + 3 tablespoons granulated white sugar
2 tablespoons unsweetened cocoa powder
2 large eggs

CHOCOLATE CAKE:
1 3/4 cups all-purpose flour
1 1/2 cups granulated white sugar
2/3 cup unsweetened cocoa powder (not Dutch process)
1 1/2 teaspoons baking soda
1/2 teaspoon baking powder
1/2 teaspoon salt
1 teaspoon instant espresso powder
3 large eggs, at room temperature
1 1/4 cups buttermilk, divided
3/4 cup unsalted butter, at room temperature
1 teaspoon vanilla extract

CHOCOLATE SOUR CREAM FROSTING:
2 cups semisweet chocolate chips
1/2 cup (1 stick) unsalted butter, at room temperature
1 cup sour cream
2 tablespoons light (white or golden) corn syrup