Preheat the oven to 350˚F. Lightly spray an 8×8 inch baking pan.
In a medium bowl, beat together the vegetable oil, 1 cup sugar, vanilla and 2 eggs until fully combined. Mix in the flour, cocoa, baking powder and salt until fully incorporated.
In a separate bowl, mix together the cream cheese, 1 egg and 1/3 cup sugar until smooth.
Pour the brownie batter in the prepared pan, and dollop the cream cheese mixture over top. Using a knife, swirl the two batters together.
Bake for 35-40 minutes, or until a toothpick inserted comes out clean.