Preheat oven to 325°F. Grease a 9-inch springform pan and set aside.
In a medium bowl, mix together cornbread crumbs, 1/3 cup sugar, and melted butter. Press onto the bottom of the prepared pan and bake for 10 minutes. Set aside to cool.
In a large bowl, beat 2 containers of Norman's Kosher Cholov Yisroel Cream Cheese and peanut butter until smooth. Add 1 cup sugar and mix well. Add eggs, one at a time, beating well after each addition. Stir in vanilla and heavy cream. Fold in chopped peanut butter cups.
Pour mixture into the prepared crust and bake for 45-50 minutes or until the center is almost set. Turn off the oven and leave the cheesecake in for an additional 10 minutes.
Remove from oven and run a knife around the edge to loosen the cheesecake. Let it cool completely on a wire rack. Chill in the refrigerator for at least 6 hours or overnight.
When ready to serve, top with additional chopped peanut butter cups.
Enjoy this delectable Peanut Butter Cup Cheesecake with Cornbread Base!