Ingredients
Bring 4 to 6 cups water to a boil in a shallow saucepan (about 8 inches wide and 3 inches deep). With a pushpin or thumbtack, prick a small hole in the rounder end of each egg (this will help prevent the shells from cracking during cooking). Using a small sieve, lower the eggs into the boiling water, and let it come back to a simmer. Cook for about 6 minutes. Pour the water out and shake the pan to crack the eggshells. Cool thoroughly.
Gently shell the eggs (to prevent breaking them) under cold running water.
Preparation
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.
Put the spinach on a chopping block and coarsely chop.
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.
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.
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.
Preheat the broiler. Add the egg yolk to the sauce, whisking very fast and hard.
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.
