Place unpeeled potatoes in a large saucepan, and cover by 2 inches with cold water.
Add 1 tablespoon salt, and bring to a boil. Reduce heat to medium high, and cook until tender, about 40 minutes.
Meanwhile, fill another large saucepan with cold water, add 1 tablespoon salt, and bring to a boil. Prepare an ice bath by filling a large bowl with ice and water. (These are for cooking and cooling the gnocchi.)
Drain potatoes, and peel while still hot, holding them with a clean kitchen towel. Pass potatoes through a potato ricer or a food mill fitted with the finest disk onto a lightly floured work surface. Make a well in the center of the mound of potatoes, and sprinkle flour evenly over the potatoes. Break eggs into the well, and add 2 1/2 teaspoons salt and the pepper. Using a fork, lightly beat eggs, and incorporate the remaining ingredients to form a dough. Knead lightly on the work surface until the dough is soft and smooth.
Lightly dust the work surface with flour. Divide dough into 4 balls, and shape each ball into a rope 3/4 inch in diameter.
Cut each rope into 1-inch pieces. Shape the gnocchi: Hold a dinner fork in one hand, and use your index finger to hold a cut edge of a piece of gnocchi against the curved back of the tines of the fork. Press into the center of the gnocchi with your index finger to make a deep indentation. While you are pressing the piece against the tines, flip it away over the tip of the fork, allowing the gnocchi to drop to the work surface. If the gnocchi becomes sticky, dip fork and index finger into flour. The finished gnocchi will have ridges on one side and a depression on the other. At this point, gnocchi can be refrigerated on a lightly floured baking sheet for several hours before boiling and serving.
To cook gnocchi, drop half of them into the boiling water, and cook until they float to the surface, about 2 to 3 minutes.
Remove with a slotted spoon, and place in the ice bath for about 20 seconds.
Transfer from ice bath, to a colander, and repeat process with the other half of the dough.
