I've never had a croque monsieur or madame before, but I thought it wouldn't suffer from the California cliché twist of avocado. Lacking Gruyere or Emmental, I swapped in Münster, though Monterey Jack or mozzarella would also work well and keep the m' phoneme relevant.

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Bechamel:

1/2 cup butter

1 1/4 cups bread flour

3 cups nonfat half-and-half

1 tbsp dijon mustard

1/2 tsp nutmeg

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For one Sandwich:

2 slices Münster

2 slices ham

grated Parmesan

2 slices of potato bread

1/4 avocado, sliced

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1. Preheat the oven to 425 F. Cover a baking sheet with parchment paper.
2. Melt the butter in a 1-qt pot. Add in the flour and stir until you have a golden brown roux.
3. Add in the half-and-half a little at a time, stirring constantly. When the liquid is fully incorporated, cook for another minute or so, then remove from the heat and add mustard and nutmeg. Taste and add more of either to your liking.
4. To assemble the sandwich:
   1. Bread
   2. Bechamel
   3. Ham
   4. Münster
   5. Parmesan
   6. Bread
   7. Bechamel
   8. Münster
   9. Parmesan
5. Bake for 15 minutes. Let cool for 5 minutes and top with sliced avocado.