Prepare cheesecake filling first by combining softened cream cheese, powdered sugar, and vanilla extract and stirring until smooth and combined.
Drop by 1 Tablespoon-sized scoops onto a wax paper lined plate or baking sheet and transfer to the freezer to chill while you prepare your cookie dough.
In a large bowl using an electric mixer (or using a stand mixer), beat together butter and sugars until creamy and well-combined.
Add eggs and vanilla. Stir well.
In a separate bowl, whisk together flour, cornstarch, baking soda, baking powder, and salt.
Gradually stir dry ingredients into the butter mixture until completely combined.
Stir in chocolate chips.
Scoop 3 Tablespoons of cookie dough and form the dough into a ball by gently rolling it between your palms. Make a crater in the center of the dough with your thumb (if the dough is too sticky to manage, place it in the refrigerator for 15-30 minutes before proceeding).
Remove a single scoop of cheesecake mixture from your freezer and gently press it into the crater you just created (see photo in post or video for visual, if needed).
Form the dough into a ball around the cheesecake, concealing the cheesecake filling in the center of the cookie. Make sure there are no cracks and no filling is visible (you just want to make sure the filling can't "escape" you can add a bit more dough, if needed!).
Place cookie dough on a wax paper lined plate and chill in the freezer for 15 minutes (this will keep it from spreading).
Meanwhile, preheat oven to 375F (190C).
After dough has chilled and oven has preheated, place cookie dough balls on parchment paper lined baking sheet, spacing cookies at least 2.5" (6 cm) apart.
Bake for 12-13 minutes or edges are beginning to turn golden brown.
Allow cookies to cool completely on cookie sheet before serving.