Preheat oven to 375 degrees F. Line two cookie sheets with parchment paper.
Stir flour, graham cracker crumbs, baking soda and salt together in a bowl.
Cream butter and both sugars in a mixing bowl using high speed of an electric mixer; add vanilla extract and egg and beat for another 30 seconds.
Using a mixing spoon, stir in flour/crumb mixture. When flour mixture is incorporated, stir in chocolate chips.
Drop dough by rounded tablespoons, spacing 3 inches apart, onto cookie sheets; bake one sheet on center rack for 8 minutes. Remove from oven and quickly press marshmallows and milk chocolate into cookies. Return to oven and cook until done (about 3 more minutes).
Let cool on a cookie sheet for 3 minutes, then transfer to a wire rack to cool. Repeat with remaining cookie dough.