Begin by bringing 4-6 cups of water to a boil. Prick the round end of each egg, then lower them into the boiling water. Reduce heat to a simmer and cook for 6 minutes. Cool the eggs under cold running water.

In a separate pot, bring salted water to a boil. Add 2 pounds of spinach and cook for 1 minute. Drain, cool under cold water, and chop. Sauté in a skillet with 3 tablespoons of butter, 2 teaspoons of salt, 1/2 teaspoon of pepper, and 1/4 teaspoon of nutmeg for 2 minutes.

In an ovenproof dish, arrange the sautéed spinach as the base. Place the cooled eggs on top and sprinkle with 3 tablespoons of cheese.

In a saucepan, melt 1 tablespoon of butter over medium heat. Stir in 1 tablespoon of flour, add 1 cup of half-and-half gradually, and cook until boiling while whisking. Add 1/2 teaspoon of salt and 1/4 teaspoon of pepper. Cool sauce for 6-8 minutes, then whisk in egg yolk.

Coat eggs with Mornay sauce, sprinkle with 1 1/2 tablespoons of Parmesan, and broil for about 5 minutes until bubbling and browned. Serve immediately.