In a deep saucepan, add the ghee or butter and heat over medium heat until melted. Add the flour and stir quickly, continuing to mix until the flour is fragrant and lightly toasted.

Remove the saucepan from the heat briefly. Gradually add the milk. For the last cup of milk, beat the egg well and mix it into the milk, then add to the saucepan. Return the saucepan to the heat and whisk quickly to prevent lumps.

Add salt, black pepper, and nutmeg (add the bouillon cube if using). Continue whisking quickly to keep the sauce smooth.

Keep stirring until the béchamel thickens to your desired consistency.

Remove from heat and use with dishes like baked pasta, vegetables, or other recipes that call for béchamel sauce.