Make the cookie dough: Preheat oven to 325 degrees. Cream the butter, white sugar, brown sugar, and peanut butter until smooth and fluffy. Add the egg and beat until incorporated. In a separate bowl, mix the flour, baking soda, and salt. Slowly add the flour mixture in with the butter and sugar, mixing well after each addition. Stir in the oats and chocolate chips.
Make the cheesecake filling: Cream the cream cheese, egg, sugar, and vanilla until smooth.
Press half to two-thirds of the cookie dough in the bottom of a greased 9x13 dish. Pour the cheesecake filling over the dough. Crumble the remaining dough and sprinkle over the top.
Cover with foil and bake for 20 minutes; remove foil and bake for another 15-20 minutes, or until tops is lightly browned and cheesecake layer is set. Serve warm or cold and store leftover bars in refrigerator.