Preheat the oven to 350 degrees F (175 degrees C). Line an 8-inch-square baking pan with heavy duty aluminum foil.
Slice off 1/3 the dough, creating 2 portions. Pat the bigger portion into the bottom of the prepared pan. Reserve the smaller portion for topping.
Combine peanut butter and vanilla extract in a bowl. Beat using an electric mixer on low speed until creamy. Add confectioners' sugar slowly, 1 tablespoon at a time, beating well after each addition. Add chocolate chips.
Drop spoonfuls of the peanut butter mixture onto the cookie dough in the baking pan and pat down to cover the dough. Crumble reserved dough into pebble-like chunks; drop over the peanut butter layer. Pat down slightly.
Bake in the preheated oven until edges are golden, about 30 minutes. Let cool in the pan. Lift cookies out by the aluminum foil and cut into bars.