Boil the Eggs: Bring 4–6 cups of water to a rolling boil in a shallow saucepan. Prick the round end of each egg, then gently lower them into boiling water and simmer for 6 minutes.

Ice Bath Transition: Transfer the eggs to a cold water and ice bowl to stop cooking. Let sit for 5–7 minutes and peel under running water.

Prepare the Spinach: Boil about 1/2 inch of water in a pot. Add spinach, cover, wilt for 1 minute, then drain and run cold water over it.

Sauté the Spinach: Chop cooled spinach. In a skillet, melt butter, add spinach, salt, black pepper, and nutmeg. Sauté for 2 minutes.

Layer Spinach and Eggs: Preheat broiler. Layer sautéed spinach in an ovenproof dish, then arrange peeled eggs on top.

Prepare the Mornay Sauce: Melt butter in a saucepan, stir in flour to create a roux, cook 1 minute. Whisk in half-and-half, season, simmer for 6–8 minutes, then whisk in the egg yolk.

Assemble for Broiling: Pour Mornay sauce over eggs, sprinkle with Gruyère cheese.

Broil to Perfection: Broil for about 5 minutes until cheese is bubbling and golden.