Melt the butter in a medium saucepan over medium heat until foamy but not browned.

Add the flour all at once and whisk immediately to form a roux, cooking for 1-2 minutes until it turns a nutty color.

Reduce heat to medium-low. Slowly whisk in about 1/4 of the cold milk until the mixture is smooth.

Stir in the remaining milk in a steady stream while whisking constantly. Cook until it thickens enough to coat the back of a spoon (about 5-7 minutes).

Remove from heat, then stir in mustard powder, garlic powder, Worcestershire sauce, cayenne (if using), and half the black pepper.

Gradually add the shredded cheddar cheese, waiting for each handful to melt completely before adding the next.

Taste and adjust seasoning with salt and pepper. If the sauce is too thick, thin it out with a splash of milk.

Serve immediately over hot, crispy fries.