Make the cookie layer: cream the butter and both sugars on high speed for 3-5 minutes, until light and fluffy.
Add the egg and vanilla and beat again. Fold in the flour and chocolate chips. Use a spoon to 'dollop' the cookie dough on top of the cheesecake layer.
Bake for 35-40 minutes, until the edges of the cheesecake are just turning golden and it is only a little wobbly in the middle. Let set for at least an hour before slicing.