Put the potatoes, whole and skin-on, in a large pot with cold water covering them by at least 2-inches. Bring to a steady boil and cook just until they are easily pierced with a fork or sharp knife blade—don’t overcook or let the skins burst.

Lift potatoes from the water and let them drain briefly. Peel and press through the ricer or food mill as soon as you can, while they’re still very hot, so their moisture will evaporate. Spread the riced potatoes in a thin layer on a baking sheet or tray, sprinkle the salt all over and let them cool and dry for at least 20 minutes, preferably 2 to 3 hours.

To mix the dough, pile the dried potatoes in a large loose mound on a board or marble work surface. Pour the beaten eggs over them then sprinkle 1 cup of the flour on top. Using your hands, work in the eggs, mixing and moistening the flour and potatoes. Gather into a single mass and knead for several minutes, scraping in sticky bits from the board and your hands. Incorporate additional flour in small amounts, only as needed, until the dough is smooth, soft and only slightly sticky. Avoid adding too much flour which will make the gnocchi heavy and dry. Cover the dough with a towel and form into gnocchi or offelle as soon as possible.

To shape traditional gnocchi, cut the finished dough into 3 or 4 pieces. Dust the work surface and your hands with flour. Roll one piece under your hands into a thick cylinder and gradually stretch it to long rope, about 2/3-inch thick. With a sharp knife or dough cutter, slice the rope, crosswise, into ½-inch lengths; sprinkle pieces with flour.

Hold a dinner fork, tines downward at an angle to your work surface. Place one of the cut sides of a piece of dough against the tines. With your lightly floured thumb, press into the dough on the other cut side and at the same time push it off the end of the fork onto a floured board. It will be hollow and curved where you pressed it and ridged on the side that rolled off the fork. Press and roll the other cut pieces into gnocchi, dust them with flour and set in a single layer on a floured tray, not touching.

Small gnocchi should be cooked (or frozen) as soon as they are all shaped. Follow the instructions for cooking and dressing offelle with sage butter and grated cheese.