Preheat oven to 350º F. Line a 9-inch square pan parchment paper (or spray with non-stick spray). Set aside.
In a mixer combine butter and both sugars together. Beat until light and fluffy about 2 minutes. Add egg and vanilla, mix until well combined. Mix in the flour, cornstarch, baking soda, and salt until just incorporated. Fold in chocolate chips.
Make the cheesecake layer by beating together the cream cheese and sugar together until fully blended. Add the egg and vanilla, and beat for 1 minute until smooth and creamy.
Press about 2/3rds of the cookie dough into the prepared pan. Pour cream cheese mixture over the dough.
Take small balls (about 1 tsp) of the remaining dough and scatter them over the top of cream cheese mixture. You will have holes, and that is perfectly fine.
Bake for 35-40 minutes, until golden and a toothpick comes out clean.
Cool completely before serving.
Store leftovers in the fridge.
Notes
You can use store bought cookie dough for a short cut.