Heat butter in a medium saucepan over medium heat until foaming. Add flour and cook, whisking constantly, 1 minute. Whisk in warm milk, ½-cupful at a time. Bring sauce to a boil, reduce heat, and simmer, whisking often, until the consistency of cream, 8–10 minutes; add nutmeg and season with salt. Remove from heat, transfer to a medium bowl, and press plastic wrap directly onto surface; let cool slightly.