Melt butter in a saucepan over medium heat. Whisk in flour and cook for 1 minute stirring constantly.
Gradually whisk in milk until smooth and bring to a gentle boil. Cook for 2-3 minutes, whisking frequently until thickened.
Remove from heat. Add shredded cheddar cheese and whisk vigorously until melted and smooth.
Season with dry mustard, salt, and pepper.