Make the sauce: In the same pan, reduce the heat to medium and melt the butter. Add the flour and cook, whisking, for about 3 minutes. Slowly whisk in the milk and chicken broth until smooth; simmer, whisking constantly, until slightly thickened, about 5 minutes. Whisk in 1/2 teaspoon salt, the nutmeg and 1/4 teaspoon of white pepper.