In a medium saucepan, melt the butter over medium heat.
Whisk in the flour and cook for 2-3 minutes, stirring constantly, until the mixture forms a smooth roux.
Gradually pour in the milk and heavy cream, whisking continuously to prevent lumps from forming.
Bring the mixture to a simmer and cook, stirring occasionally, until thickened to a creamy consistency, about 5-7 minutes.
Remove the saucepan from the heat and gradually stir in the shredded cheddar cheese, a handful at a time, until fully melted and incorporated.
Season the cheese sauce with salt and black pepper, adjusting to taste.
Serve the Creamy Cheddar Cheese Sauce warm over your desired dishes, such as pasta, steamed vegetables, or as a dip.