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1
Preheat the oven to 400 degrees F. Grease an 8-inch square baking dish.(or larger dish)
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2
Melt 6 tablespoons of butter in a large skillet over low heat until bubbling. Whisk in the flour and cook for 1 minute.
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3
Slowly whisk in the milk and cook until thick and bubbling, 3 to 5 minutes more.
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4
Whisk in the mustard, salt, pepper, and nutmeg.
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5
Pour a thin layer of the sauce into the prepared baking dish and cover it with 5 or 6 slices of the bread, then slices of the ham and an even layer of the Gruyere.
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6
Repeat the layers once more, ending with a third layer of sauce to cover all.
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7
Bake the casserole for 30 minutes.
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8
Working in 2 batches, melt butter in a large skillet over medium-high heat.
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9
Crack 3 eggs into the skillet and season with salt and pepper, to taste. Cook until the whites are nearly set, about 3 minutes.
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10
Carefully flip the eggs and continue cooking until the whites are slightly set, they will cook more under the broiler.
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11
You're going to top portions of the casserole with a fried egg. Repeat with the remaining 3 eggs.
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12
Top with Gruyere and put in the oven for a few minutes until cheese melts, watching carefully so it does not burn.
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13
Cut into 6 pieces so each has an egg and serve.
