Warm the milk in a separate pot until it’s steaming but not boiling. Don’t rush this step — we’re making velvety magic, not a spicy soup.
Melt the butter in a saucepan over medium heat. Once it sizzles, whisk in the flour. Cook for about 1 minute to make a smooth roux—don’t let it brown, we’re going for pale perfection.
Slowly pour in the warm milk, whisking constantly. Keep stirring until the mixture thickens and coats the back of a spoon. If it thins out, keep whisking; patience is a virtue here.
Season with salt, a pinch of nutmeg, and pepper. Taste and adjust. If you’re adding cheese, stir it in now until melted and glossy.
Remove from heat and serve immediately, or cover with a light film to keep it warm. If it thickens too much, whisk in a splash of milk.