In a saucepan, melt the butter over medium heat.
Stir in the flour, salt, black pepper, and ground mustard until well combined, creating a smooth paste.
Gradually whisk in the milk, ensuring no lumps form.
Continue to cook and stir until the mixture thickens, usually around 5-7 minutes.
Reduce the heat and add the shredded cheddar cheese, stirring until the cheese is completely melted and the sauce is smooth.