Ingredients:

  • 2 tablespoons (30g) unsalted butter (for béchamel)
  • 2 tablespoons (15g) all-purpose flour, plus more if needed (for béchamel)
  • 2 cups (473ml) whole milk, warmed (for béchamel)
  • 1/4 teaspoon freshly grated nutmeg (for béchamel)
  • Salt and freshly ground black pepper to taste (for béchamel)
  • 4 slices (approx. ½ inch thick) sourdough bread
  • 2 tablespoons Dijon mustard
  • 4 slices (approx. 4oz/113g total) good quality cooked ham
  • 4 slices (approx. 4oz/113g total) Gruyère cheese, grated (or Emmental)
  • 2 tablespoons (30g) unsalted butter, softened
  • 2 large eggs
  • Olive oil or butter for frying the eggs
  • Optional: Chopped fresh parsley, for garnish

Instructions:

  1. Make the Béchamel: Melt butter in saucepan. Whisk in flour and cook for 1-2 minutes to form a roux. Gradually whisk in warm milk until smooth. Simmer gently, stirring constantly, until thickened (about 5-7 minutes). Stir in nutmeg, salt, and pepper. Set aside; keep warm. Add more flour to roux for thickness if needed.
  2. Assemble the Sandwiches: Spread Dijon mustard on each slice of sourdough. Layer 2 slices of ham and 2 slices of Gruyère on two of the bread slices. Top with the remaining bread slices.
  3. Butter and Griddle: Spread softened butter evenly on the outsides of the assembled sandwiches.
  4. Griddle the Sandwiches: Place the sandwiches in a preheated skillet or griddle pan over medium heat. Cook until golden brown and the cheese is melted, about 3-4 minutes per side. Press down gently with a spatula to ensure even browning.
  5. Fry the Eggs: While the sandwiches are griddling, heat olive oil or butter in a separate frying pan over medium heat. Fry the eggs to your desired doneness (sunnyside up, over easy, etc.).
  6. Top with Béchamel and Egg: Place the griddled sandwiches on plates. Spoon a generous amount of béchamel sauce over each sandwich. Carefully place a fried egg on top of each sandwich.
  7. Garnish and Serve: Garnish with chopped fresh parsley (if desired) and serve immediately.