Image of Croque Madame Sandwich

Croque Madame Sandwich

Prep Time: 15 min
Cook Time: 25 min

Ingredients

  • 4 tablespoons salted butter, softened, divided
  • 1 ½ tablespoons all-purpose flour
  • 1 cup milk
  • 2 ounces grated Gruyere cheese
  • ¼ teaspoon salt, or to taste
  • ¼ teaspoon ground black pepper, or to taste
  • ⅛ teaspoon ground nutmeg
  • 4 slices white bread, lightly toasted
  • 2 teaspoons Dijon mustard
  • 2 thin slices Black Forest ham
  • 2 large eggs
  • 1 tablespoon water
  • 1 teaspoon chopped fresh dill, or to taste