1. Preheat oven to 325 degrees. Butter a 9-by-13-inch baking pan; set aside. Make the cream cheese batter: Beat cream cheese, butter, and sugar in the bowl of an electric mixer fitted with the paddle attachment until well blended. Add eggs, one at a time, beating well and scraping down the sides of the bowl at least once. Add vanilla, and beat until combined. Using a large rubber spatula, fold in the flour and chocolate chips.

2. Make the chocolate batter: Melt chocolate and butter in a medium heatproof bowl set over a pan of barely simmering water. Remove bowl from heat, and let cool completely.

3. In a large bowl, using a handheld whisk, beat the eggs, gradually adding the sugar, until mixture is thick and pale. Whisk in the cooled chocolate mixture. Add the vanilla, and combine well.

4. Combine flour, baking powder, and salt in a medium bowl, and fold into the chocolate mixture. Fold in chocolate chips. Measure out about 1/2 cup chocolate batter, and set aside. Spoon the rest of the batter into prepared baking pan, and spread cream cheese batter evenly over the top. Drop reserved chocolate batter in dollops on top. Run a knife or offset spatula all the way through the batters to create a swirling effect.

5. Bake until a cake tester inserted near the edges comes out clean, about 35 minutes. The center will still be fairly soft, but will continue to firm after being removed from the oven. Transfer to a wire rack; let cool in pan before cutting into squares and serving.