1. In a medium, heavy saucepan, whisk flour to remove any lumps.
2. Gradually add 1 cup milk, whisking until smooth.
3. Add remaining milk and the nutmeg.
4. Whisk over medium heat until thickened and comes to a boil, about 4 minutes.
5. Remove from heat and stir in Parmesan and butter.
6. Season to taste.