Stir sugar, cocoa, and evaporated milk together in a large nonstick saucepan over medium heat until mixture comes to a boil; boil for 5 minutes, stirring constantly. Remove from heat and stir butter and marshmallow creme into cocoa mixture. Quickly stir graham cracker crumbs into mixture.
Drop cookies by the spoonful onto waxed paper; let stand until firm. Store in airtight containers.