Stir butter and sugar together in a mixing bowl. Mix until creamed and resembles a sugary, buttery paste, 4 to 5 minutes. Add oats and flour; stir until flour and oats are incorporated into the butter-sugar mixture and mixture resembles coarse crumbs, 4 to 5 minutes. Pour in milk; stir until mixture is wet and creamy, like a thick spreadable batter, 3 to 4 minutes.