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Melt the butter in a medium saucepan over medium heat.
When the butter is hot and the foaming subsides, add the flour, and ground mustard and cook for 2 minutes, stirring constantly.
Gradually add the milk and continue cooking until thickened and bubbling, stirring constantly.
Add the cheese and continue cooking until melted, stirring frequently.
Thin the sauce with extra milk, if necessary.
Add salt and freshly ground black pepper, to taste.