1. Preheat oven to 350°F (176°C) and line a 9 inch square baking pan with aluminum foil.
2. Cream butter and sugars together until light and fluffy, about 3-4 minutes.
3. Add egg and vanilla extract and mix until well combined.
4. Combine flour, cinnamon, cornstarch and baking soda in a medium sized bowl.
5. Slowly add the flour mixture to butter mixture and mix until well combined.
6. Stir in the old fashioned oats. The dough will be thick. Set aside.
7. To make the cheesecake filling, beat the cream cheese, sugars and cinnamon together until smooth.
8. Add the egg and mix until well combined.
9. Press just over half of the cookie dough into the bottom of the pan.
10. Add a layer of slices peaches on top of the cookie dough
11. Spread the cheesecake mixture evenly over the peaches.
12. Crumble the remaining cookie dough on top of the cheesecake.
13. Bake for 29-32 minutes. Edges should be lightly browned and center may still be a bit jiggly but will firm as it cools.
14. Allow to cool completely in refrigerator before slicing. Store in covered container in refrigerator.