French Onion Croque Madame

Deselect All

Onions:

4 yellow onions, thinly sliced

2 garlic cloves, unpeeled

4 sprigs thyme

3 tablespoons olive oil

2 tablespoons brandy

1 tablespoon maple syrup

Kosher salt

Freshly ground black pepper

1 teaspoon white wine vinegar

Sandwiches:

1 1/2 cups milk (375 milliliters)

2 tablespoons butter

2 tablespoons flour

1 teaspoon kosher salt

1/4 teaspoon freshly ground black pepper

1/2 teaspoon herbes de Provence

Pinch freshly grated nutmeg

1/4 cup finely grated Parmigiano-Reggiano cheese (25 grams)

1 1/4 cups grated Gruyère or Emmental cheese, divided (150 grams)

8 slices sourdough multigrain rye, toasted, such as Stonemill

4 teaspoons Dijon mustard

8 thin slices ham, optional (about 150 grams)

4 eggs

Butter, for frying eggs

Fresh thyme, for garnish