Special Equipment: Steaming basket
Serving Suggestion: French baguette, sliced
Preheat oven to 350 to 375 degrees F.
In a large pot fitted with a steaming basket, bring 1-inch of water to a boil. Place the endives in the basket, cover, and let cook until very soft, about 10 to 15 minutes. Transfer to a colander and let drain, pushing down on the endives with a clean kitchen towel until as much of the water as possible has been expelled. Do not mush the endives!
In a large frying pan over medium-high heat, melt 2 tablespoons of the butter. When the foam has subsided, add the endives and cook, turning occasionally, until brown and caramelized on all surfaces. Remove from heat and wrap each endive in 1 slice of the ham. Set aside.
In a small saucepan over medium heat, melt the remaining 2 tablespoons of butter. When the foam has subsided whisk in the flour and cook 1 minute, being careful not to brown the flour. Whisk in the milk in a slow, steady stream. Bring to a boil whisking constantly, then reduce heat to medium-low and simmer until thickened, about 8 minutes. Season with a generous amount of pepper and the nutmeg.
Spread about 1 cup of the sauce over the bottom of a 9 by 13-inch flameproof ceramic baking dish, then arrange the ham-wrapped endives on top in a single layer. Cover with the remaining sauce and the cheese. Bake until the cheese is melted and the sauce is bubbling, about 30 minutes. Turn on the broiler, transfer the pan to the top rack, and broil until the cheese has patches of golden goodness - about 2 minutes. Serve hot with generous amounts of sauce and baguette slices.