Boil in a covered pot with a pinch of salt for about 10 minutes, without adding water other than what clings to it from washing.
Cool and squeeze to remove excess water. Chop coarsely and sauté in a pan with 3 1/2 tablespoons butter.
Prepare the béchamel sauce: Melt remaining 3 1/2 tablespoons of butter in a pan. Add sifted flour and cook over low heat for one minute, stirring with a whisk. Add milk in a constant stream and bring to a boil, stirring constantly. Season with salt and a dash of nutmeg. Cook for a few more minutes until thick. Add 1/2 cup Parmigiano.
Place spinach in a buttered baking dish. Create four wells with a spoon and drop one egg in each.
Season eggs with salt and pepper and cover everything with béchamel sauce.
Sprinkle with remaining Parmigiano Reggiano and bake in a preheated 350°F oven for about 20 minutes.