Mix cream cheese, sugar, eggs, and vanilla together in a bowl until smooth and well blended.
Spread 1 roll of cookie dough on the bottom of a 9x13-inch baking pan to form the base. Spread cream cheese mixture evenly on top. Pinch off small pieces of the remaining cookie dough and distribute them on the cream cheese mixture.
Bake in the preheated oven until cream cheese mixture is set and cookies on top are golden brown, 30 to 45 minutes. Let cool before serving, about 30 minutes.