Add butter to a saucepan. Place over medium heat and melt butter.

Add flour, to make a roux. Cook, stirring constantly with a whisk, for about 1 minute, or until it no longer smells like raw flour but has a slightly nutty smell and a pale golden color.

While whisking constantly, add milk. Mix until fully incorporated and there are no lumps.

Continue cooking and stirring until the sauce starts to thicken and comes to a simmer.

Reduce the heat to low. Continue simmering and stirring until the sauce is thick, about 4 minutes.

Season with salt and pepper, to taste.

Remove from heat. Set aside.