Beat the sugar, butter, vanilla and 4 tablespoons of the milk in a mixing bowl on low speed until combined. Add the remaining milk, 1 tablespoon at a time until smooth. Switch to high speed and beat until the frosting is a spreadable consistency, but still thick enough so it's not too runny. Add more milk, if needed, 1 tablespoon at a time. If it gets too runny, add more powdered sugar, as needed, 1/4 cup at a time. Use an offset spatula to spread frosting on the cookies, leaving 1/4-inch edge.