1. Mix together the carrot cake mix, 1 egg, and the softened butter until thick.
2. Press the mixture into the bottom of an 8x8 inch pan.
I would suggest using a spatula coated with flour to layer it in the bottom of the pan. The flour will keep it from sticking as this mixture gets really sticky.
Making the Cheesecake:
1. Beat the cream cheese, 2 eggs, sugar, and vanilla until smooth.
2. Layer the cheesecake mix onto the cake layer and bake 25-30 minutes or until the edges start to pull away from the pan.