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1
Preheat the oven to 400 degrees F. Grease an 8-inch square baking dish.
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2
Melt 6 tablespoons of butter in a large skillet over low heat until bubbling.
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3
Whisk in the flour and cook for 1 minute.
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4
Slowly whisk in the milk and cook until thick and bubbling, 3 to 5 minutes more.
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5
Whisk in the mustard, salt, pepper, and nutmeg.
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6
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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7
Repeat the layers once more, ending with a third layer of sauce to cover all.
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8
Bake the casserole for 30 minutes.
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9
Remove it from the oven and cut into 6 equal pieces.
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10
Working in 2 batches, melt 1tablespoon of butter in a large skillet over medium-high heat.
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11
Crack 3 eggs into the skillet and season with salt and pepper, to taste.
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12
Cook until the whites are nearly set, about 3 minutes.
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13
Carefully flip the eggs and continue cooking until the whites are completely set, about 1 minute more.
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14
You're going to top each portion of the casserole with a fried egg.
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15
Repeat with the remaining 3 eggs and 1 tablespoon butter.
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16
Top with Gruyere and it in the oven for a few minutes until cheese melts.
