Preheat the oven to 350°F. Line two muffin pans with paper liners and set aside.
In a large bowl, cream together the butter and sugars until light and fluffy. Add in the egg and vanilla, and mix until fully incorporated.
In a separate bowl, mix together the flour, cornstarch, baking soda and salt. Mix the dry ingredients into the wet ingredients until fully combined. Fold in the chocolate chips.
Scoop 1.5 Tablespoons of cookie dough into the prepared muffin pans, and pack it in. Bake for 10 minutes in the preheated oven.
Meanwhile in a separate bowl, cream together the cream cheese, white sugar, egg and vanilla until smooth.
Scoop 1 Tablespoon of cheesecake mixture on each cookie cup, and continue to bake for around 18 more minutes. Remove from oven and allow to cool.