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