In a medium-sized bowl, with an electric beater on medium speed, combine the cream cheese, eggs, sugar, and vanilla until fluffy. Spoon over the brownie batter, then top with the remaining half of the brownie batter.

Using a table knife, cut through the batter and swirl to create a marbled effect. Bake for 35 to 40 minutes, or until a wooden toothpick inserted in the center comes out clean. Allow to cool, then cut into bars and serve, or cover and chill until ready to serve.