1. Preheat oven to 325 degrees. Lightly butter an 8-by-8-inch glass baking dish, and set aside. Into a medium bowl, sift together flour, salt, and baking soda; set aside.

2. Make chocolate batter: In a large heatproof bowl set over a pan of simmering water, heat 1/2 cup butter and 1/2 cup chocolate chips until they are melted. Remove from heat, and stir in 1 cup sugar. Add half the flour mixture, and stir to combine. Add the whole eggs and 2 teaspoons vanilla, and stir to combine. Mix in remaining flour mixture until it is well combined. Measure out 1/2 cup batter, and set aside.

3. Make cream-cheese batter: In the bowl of a food processor fitted with the metal blade, combine the cream cheese, remaining 1/4 cup sugar, remaining 2 tablespoons butter, the egg yolks, and remaining 3/4 teaspoon vanilla. Process until mixture is smooth and well combined. Transfer to a medium bowl. Stir in remaining 1/2 cup chocolate chips.

4. Pour chocolate batter into the prepared baking dish. Spoon the cream-cheese mixture over the chocolate batter, spreading it in an even layer to the edges with an offset spatula. Top with reserved 1/2 cup chocolate batter. Run a knife through the mixture to swirl, as desired. Bake until golden brown and the center is set when touched with your finger, 45 to 50 minutes. Transfer baking dish to a wire rack to cool. Cut into squares, and serve.