Set up grill for indirect cooking over medium heat. Spray 9 by 13-inch foil pan with cooking spray; set aside.
In a large mixing bowl, beat with an electric mixer on low speed, cake mix, butter, egg, and food coloring until combined. Press cake mixture into prepared pan; set aside.
In a medium mixing bowl, beat cream cheese and sugar on medium speed until creamy. Add eggs and vanilla, beat to combine. Spread cream cheese mixture over cake layer.
Place foil pan in a second foil pan for stability and insulation. Place on hot grill away from heat. Cover and bake 40 to 50 minutes. Rotate pan halfway through baking.
Remove from grill and cool completely before cutting.
INDOOR: Preheat oven to 350 degrees F. Spray 9 by13-inch baking pan lightly with cooking spray; set aside. Prepare bars as directed. Bake in preheated oven for 40 to 45 minutes, or until bars barely start to pull away from sides. Cool completely before cutting.