Preheat the oven to 325°F. Line an 8 inch square baking pan with parchment paper or foil allowing a little overhang and spray with nonstick cooking spray. Set aside.
Mix the melted butter and graham cracker crumbs until thoroughly combined. Press the mixture into the bottom of the prepared pan. Bake in preheated oven for 6 minutes. Remove pan to a cooling rack. Do not turn your oven off.
While the crust is cooling, prepare the chocolate chip cookie dough. In the bowl of a stand mixer fitted with the paddle attachment or in a large bowl with an electric mixer, beat butter, brown sugar, granulated sugar, salt and vanilla until smooth and thoroughly combined, about 1 minute. Mix in the flour on low speed, and mix until just incorporated. Mix in the chocolate chips. Set aside.
In the bowl of a stand mixer fitted with the paddle attachment or in a large bowl with an electric mixer cream together the cream cheese and sugar until smooth. Mix in the egg and vanilla on low speed just until incorporated. Pour the cheesecake batter into the prepared crust.
Using your hand, form clumps of the cookie dough. Flatten the clumps of dough in your palms and distribute the cookie dough onto the top of the cheesecake batter. Be sure to use all of the dough. You will cover most of the cheesecake batter.
Bake for about 35-40 minutes, until the top looks dry and firm (the cookie dough) and the entire pan looks set if given a gentle shake. Move bars to a cooling rack and allow to cool completely, then refrigerate for at least 2 hours.
Lift the bars out by the overhang; slice into 12 servings. When ready to serve, top with a chocolate square, toasted marshmallow and devour!