Melt butter in a saucepan over medium heat. Stir in flour and salt, whisking until smooth and bubbly, about 1 minute.
Pour in milk while whisking. Cook until thick enough to coat a spoon, about 2-4 minutes.
Lower the heat. Gradually stir in the shredded cheddar until smooth and melted. If needed, add another splash of milk to thin it out. Serve immediately.