Melt butter in a large saucepan over medium heat. Once melted, stir in the flour until smooth. Continue stirring as the flour cooks to 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 not longer tastes gritty, 10 to 20 minutes, then season with salt and nutmeg.