Smoky Grilled Croque Madame | CarnalDish

Ingredients

• 9 slices smoked ham
• 6 slices good quality sandwich bread
• 6 ounces gruyere cheese, shredded (SEE NOTE)
• Dijon mustard
• 2 teaspoons fresh thyme leaves
• 3 tablespoons butter, softened
• Black pepper, to taste
• Sea salt, to taste
• 3 large eggs
• Olive oil
• 3 tablespoons butter
• 1 small shallot, finely minced
• 1 clove garlic, minced
• 1 1/2 cups half and half
• 3 tablespoons all-purpose flour
• 6 ounces gruyere cheese, shredded
• 3 tablespoons parmigiano-reggiano cheese (optional)
• 1/2 teaspoon fresh thyme, chopped
• pinch of nutmeg
• Sea salt and black pepper, to taste