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1
FOR THE SPINACH: Bring about 1/2 inch of salted water to a boil in a stainless steel pot. Meanwhile, remove and discard the spinach stems. Drop the leaves into the boiling water and boil, covered, for about 1 minute, until wilted. Drain the spinach in a colander and immediately refresh under cold running water to stop the cooking and keep the color. Drain again, pressing on the spinach to extract as much water as possible.
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2
Put the spinach on a chopping block and coarsely chop.
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3
Melt the butter in a skillet over high heat and cook until it turns brown. Add the spinach, salt, pepper, and nutmeg, mix well with a fork, and cook for 2 minutes.
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4
Arrange the spinach in the bottom of an ovenproof dish large enough to accommodate the eggs. Arrange the cold eggs on the spinach, with a little space between them, and sprinkle the cheese on top.
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5
FOR THE SAUCE: Melt the butter in a heavy saucepan. Stir in the flour until smooth and cook, stirring constantly, for about 1 minute, until the mixture froths, without browning. Add the half-and-half, whipping constantly with a whisk, and bring to a boil, whisking constantly. Stir in the seasonings and continue cooking over low heat for 1 minute, stirring constantly with the whisk. Cool for 6 to 8 minutes.
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6
Preheat the broiler. Add the egg yolk to the sauce, whisking very fast and hard.
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7
Coat the eggs with the sauce and sprinkle with the Parmesan cheese. Place under the hot broiler (not too close, so the eggs have a chance to get hot inside) for 5 minutes, or until the sauce is nicely browned. Serve immediately.