In a large bowl, beat together cream cheese, eggs, sugar, and vanilla extract until well mixed; set aside.
Slice cookie dough rolls into 1/4-inch slices. Arrange slices from one roll on bottom of a greased 9- x 13-inch baking dish; press together so there are no holes in dough. Spoon cream cheese mixture evenly over dough; top with remaining slices of cookie dough.
Bake 45 to 50 minutes, or until golden and center is slightly firm.
Remove from oven, let cool, then refrigerate. Cut into slices when well chilled.
Keep cookie dough refrigerated until just before slicing. You can serve the cheesecake plain, with chocolate sauce, with fudge or whipped topping...whatever's your favorite.