Melt butter in a large saucepan over medium heat. Add flour and whisk into the melted butter until smooth. Cook and stir until flour turns a light, golden, sandy color, about 7 minutes.

Increase heat to medium-high and slowly whisk in milk until thickened by the roux. Bring to a gentle simmer, then reduce heat to medium-low and continue simmering until the flour has softened and no longer tastes gritty, 10 to 20 minutes. Season with salt and nutmeg.