Combine sugar and hot coffee in a large mixing bowl, stirring until sugar dissolves; stir in 1 cup milk. Cover and freeze 8 hours.
Let thaw slightly in refrigerator; add remaining 1 cup milk. Beat at medium speed with an electric mixer until smooth. Garnish, if desired. Serve immediately.
* Substitute fat-free milk or fat-free half-and-half for regular milk or half-and-half.