Heat a skillet over medium heat. Beat egg and milk together in a pie plate or shallow dish. Pour graham cracker crumbs in a second pie plate or shallow dish.
Spread Nutella on both slices of bread. Top one slice with mini marshmallows and then put the other slice of bread on top, Nutella side down. Squish together a bit with spatula.
Place sandwich in egg mixture and turn to coat. Remove and place in graham cracker crumbs, turning sandwich to coat each side with crumbs.
Place sandwich in skillet and cook until lightly browned and the marshmallows are melted.