Gnocchi soffiati alla parigina (puffed gnoochi)

Ingredients:
1 cup of water
1/2 tsp salt
1/4 tsp grated nutmeg
2 tbsp unsalted butter, plus 1 tbsp melted
1 cup all-purpose or "00" flour
3/4 cup grated Parmigiano-Reggiano (3 oz)
3 large eggs

1. Put the water, salt, nutmeg, and tbsp butter in medium saucepan and bring to a boil. As soon as it boils, drop the flour into the mixture at once and mix quickly with a wooden spoon. Stir until the mixture forms a smooth mass that sepetates easily from the sides of the saucepan. Cook ans stir for about 40 seconds longer to dry the mixture further.
2. Transfer the dough to the bowl of a stand mixer fitted with a dough hook, or you may want to use a regular bowl and mix with your hands. Let the mixture cool slightly, and then add half of the Parmigiano-Reggiano and 1 of the eggs. Mix at low speed ( or by hand) until the egg is incorperated. Add another egg and mix again, and then repeat with third egg. At first the mixture will seem to separate, but keep mixing and eventually it will tighten up. Cover and let cool.
3. Place 3 inches of salted water in a large saucepan and heat it over medium heat until there are several small bubbles, rising around the edges ( 180 degrees F). It shouldn't boil completely; if the water is too hot the dumplings will cook too fast, which will cause them to expand and eventually (once baked) deflate. They should just pouch and expand later in the oven when baked.
4. Using 2 spoons to shape the dough or pastry bag with a plain 1-inch tip, drop the dumplings into the water; they should be 1 to 1 1/2 inches long. Work close to the surface to the water so you don't get splashed.
5. Poach the gnoochi until they rise to the surface, about 3 minutes. Lift the gnoochi out with a slotted spoon and put them in a bowl of ice water to cool. They will sink to the bottom of the bowl when cool. Drain and use them right away, or refigerate for later use.
6. Preheat the oven to 350 degrees F. Butter two 9-inch baking dishes and arrange the gnoochi in them so that they have enough space to expand in the oven ( they will almost double in size).
7. Sprinkle with the remaining Parmigiano-Reggiano, drizzle 1 tablespoon of melted butter on top, and, bake until doubled in size and golden brown, 20 to 25 minutes. Serve the gnoochi right away, before they begin to deflate.
~ Italian Cooking by Gianni Scappin, Alerto Vanoli, Steven Kolpan