Boston Cream Icebox Cake

packets instant vanilla pudding (not cook-and-serve, not sugar-free)

whipped topping, thawed (I used fat free)

cold milk (I used skim; use cow’s milk and not soy, almond, etc. because pudding won’t set up)

box graham crackers (I used Honeymaid lowfat honey)

semi-sweet chocolate chips, divided

unsalted butter

granulated sugar

milk

vanilla extract