Preheat the oven to 325° F and line a 9" square baking pan with parchment paper allowing a little overhang.
Add melted butter and graham cracker crumbs to small bowl and mix until combined. Press the mixture into the bottom of the prepared pan.
Bake in preheated oven for 6 minutes. Remove from oven and allow to cool completely.
In the bowl of a stand mixer, or using electric mixer, beat butter, brown sugar, granulated sugar, salt, and vanilla until smooth and thoroughly combined. Add in the flour and mix until just incorporated. Stir in chocolate chips.
In separate bowl, cream together the cream cheese and sugar until smooth. Add in the egg and vanilla and mix until incorporated. Pour the cheesecake batter onto the prepared crust.
Using your hands, form flat clumps of cookie dough and place onto the top of the cheesecake batter.
Bake at 350° for about 30-35 minutes, until the top feels dry and firm and the cheesecake looks set when given a gentle shake.
Move bars to a cooling rack and allow to cool completely. Chill in refrigerator overnight or for at least a couple hours to firm.
Lift the bars out by the parchment paper and cut into squares for serving.