In a mixing bowl, cream butter and sugars. Beat in egg, milk and vanilla. Combine the flour, graham cracker crumbs, baking soda, salt and cinnamon; slowly add to the creamed mixture. Stir in the chocolate chips.
Drop 1 Tbsp. of dough 2 inches apart onto parchment lined cookie sheet. Bake at 375 for 8-10 minutes or until golden brown. Remove to wire racks to cool.
Place four cookies bottom side up on a microwave safe plate top each cookie with a marshmallow. Microwave, uncovered, on high for 16-20 seconds or until marshmallows begin to puff. (do not overcook)