Melt butter in a small saucepan over medium-high heat. Add flour and whisk to a paste. Continue cooking, stirring constantly, until flour and oil have fully combined.
Whisking constantly, very slowly add in milk.
Heat, stirring, until sauce comes to a gently simmer and thickens slightly.
Reduce heat to low and cook, stirring, until thickened to a creamy consistency.
Adjust salt and pepper and season with nutmeg.