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Melt butter in a medium saucepan over medium heat until foamy. Add flour and cook, stirring, until mixture is pale and foamy, about 3 minutes. Gradually add milk, stirring until mixture is smooth. Cook, stirring, until sauce is thick and somewhat elastic, about 4 minutes. Remove from heat and whisk in mustard and nutmeg; season with salt.
DO AHEAD: Béchamel can be made 1 day ahead. Let cool; press plastic wrap directly onto surface and chill.
Preheat oven to 425°. Spread bread slices with béchamel, dividing evenly and extending all the way to the edges. Place 4 slices of bread, béchamel side up, on a parchment-lined baking sheet; top with ham and half of cheese. Top with remaining slices of bread, béchamel side up, then top with remaining cheese and sprinkle with herbes de Provence. Bake until cheese is brown and bubbling, 10–15 minutes.
DO AHEAD: Sandwiches can be made (but not baked) 1 day ahead. Cover; chill.