For the chocolate chip cookie dough: In an electric mixer fitted with the paddle attachment, beat the butter, granulated sugar and brown sugar together until creamy, about 5 minutes. Mix in the eggs and vanilla. In a separate bowl, whisk together the flour, baking soda and salt. With the mixer on low, add the dry ingredients and mix until fully incorporated. Fold in the chocolate chips.
Press half of the cookie dough mixture into the bottom of a 9-by-13-inch baking pan. Transfer the remaining cookie dough to another bowl, cover, and refrigerate while you make the filling. Rinse the mixing bowl and paddle attachment for reuse.
For the cheesecake filling: In an electric mixer fitted with the paddle attachment, beat the cream cheese and sugar together until smooth and fluffy, 5 minutes. Add the egg, sour cream, cornstarch and vanilla, and mix until combined.
Spread the cream cheese mixture evenly over the chocolate chip layer in the baking pan. In pieces, scatter the remaining cookie dough over the top until the surface is almost covered¿this will become a crust when baked
Bake until set and starting to turn golden brown on top, 45 minutes¿if it jiggles, bake longer. Transfer to a wire rack and cool completely. Chill in the refrigerator for at least 4 hours or up to overnight. Cut into squares for serving.