Prepare the Potatoes: Boil the potatoes in their skins in a large pot of salted water until fork-tender.
Drain them well and let them cool just enough to handle.
While still warm, peel the skins off and pass the potatoes through a ricer or a food mill onto a clean work surface. This creates the finest, fluffiest texture.
Form the Dough: Create a well in the center of the riced potatoes.
Add the flour, salt, and lightly beaten egg into the well.
Using your hands or a bench scraper, gently combine the , kneading just until a smooth, soft dough forms. Be careful not to overwork it! If the dough is too sticky, add a tablespoon of flour at a time, but remember it should remain soft.
Shape the Gnocchi: Divide the dough into three equal portions. On a lightly floured surface, take one portion and roll it into a long rope about 1-inch or 2. 5cm thick. Use a sharp knife or bench scraper to cut the rope into ½-inch or 1. 5cm pieces.
Repeat with the remaining dough.
Cook the Gnocchi: Bring a large pot of generously salted water to a rolling boil.
Drop the gnocchi into the water in batches, being careful not to overcrowd the pot.
Boil for 8 to 10 minutes, or until they are cooked through and float to the surface. Use a slotted spoon to remove the cooked gnocchi and drain them well.
Finish and Serve: Arrange the drained gnocchi in a single layer in a buttered casserole dish.
Drizzle generously with melted butter and sprinkle with your desired amount of grated Parmesan or Swiss cheese.
Bake in a preheated oven at 350°F or 175°C (350°F) for 15-20 minutes, until everything is heated through and the cheese is golden and bubbly. Alternatively, serve the boiled gnocchi immediately tossed with your favorite marinara or cream sauce.
Do not overwork the dough!
Knead just until it comes together to keep the gnocchi light and tender.