Melt butter in a saucepan over medium-low heat. Whisk in flour and cook, stirring, as mixture bubbles, 2-3 minutes. Add milk a little bit at a time, whisking smooth after each addition, until all of the milk has been added. Bring to a boil and reduce to a gentle simmer, whisking to prevent scorching.
Season with ½ teaspoon salt and black pepper and cook, whisking often, until sauce is thick and has lost the raw flour taste, about 5 minutes.
Remove from heat; stir in mustard and nutmeg. Taste and add more salt if needed. Use warm, or transfer to a bowl and cover the surface with plastic wrap to prevent skin from forming. Sauce can be made 3 days in advance.
Preheat oven to 400°F.
Arrange the 8 english muffin slices on a foil-lined sheet pan. Spread each evenly with béchamel sauce. Top each with 2 tablespoons of cheese, a folded ham slice, and another 2 tablespoons of cheese.
Bake for 10-15 minutes, or until sauce is bubbly and cheese is melted. Serve hot.
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