Brownies: In a large mixing bowl, combine two eggs, oil, and dry cake mix, being careful to not over mix. Set aside.
Cheesecake: Beat the softened cream cheese, sugar, one egg, sugar, and vanilla with an electric hand mixer at medium speed until the batter is smooth. Set aside.
Spray an 8x8 square baking pan with nonstick cooking spray and press ⅔ of the red velvet brownie batter onto the bottom, spreading in an even layer. (Tip: Spray your pan then add a sheet of parchment paper with the sides overhanging for easy removal of the brownies.)
Pour the cheesecake batter over the brownie layer, then sprinkle the remaining brownie batter over the top.
Bake at 350 degrees for 40-45 minutes or until a toothpick inserted in the center of the brownies comes out clean. Allow the brownies to cool completely before cutting into squares.