2 Granny Smith apples—peeled, cored and thinly sliced
1 cup water
1/4 cup maple syrup
One 3-inch cinnamon stick
2/3 cup milk
2 large eggs, beaten
Eight 1/2 -inch-thick hand-cut slices from a loaf of white bread
Dijon mustard
6 ounces sliced Gruyère cheese
1/2 pound thickly sliced smoked ham
1 to 2 tablespoons unsalted butter

Preparation:

1. In a medium saucepan, combine the apples, water, maple syrup and cinnamon stick and bring to a boil. Simmer over moderately low heat, stirring occasionally, until the apples are tender, about 6 minutes. Using a slotted spoon, transfer the apples to a bowl and let cool to room temperature.
2. In a shallow bowl, whisk the milk and eggs. Spread 4 slices of the bread with mustard. Top with half of the cheese, the ham and then the remaining cheese.
3. In a large skillet, melt 1 tablespoon of the butter over low heat. Dip the bottoms of the 4 topped bread slices in the beaten egg until just saturated and transfer to the skillet.
4. Dip the remaining slices of bread on 1 side only and place them, soaked side up, on the sandwiches. Cover the skillet and cook over moderately low heat until the bread is browned on the bottom, about 3 minutes.
5. Turn the sandwiches, adding more butter to the skillet if necessary. Cover and cook until the second side is browned and the cheese is melted, about 3 minutes longer.
6. Transfer the sandwiches to a cutting board and let stand for 5 minutes. Cut in half and serve with the maple apples.