1. Whisk flour in heavy medium saucepan to remove any lumps.
2. Gradually add 1 cup milk, whisking until smooth. Add remaining 2 cups milk and nutmeg; whisk over medium heat until mixture thickens and boils, about 10 minutes. Remove from heat.
3. Whisk in Parmesan, egg and butter. Season with salt and pepper. Can be made 1 day ahead. Cover and refrigerate. Rewarm over low heat until heated through before using; do not boil.

Makes 3 cups.