Begin by boiling the peeled potatoes in a large pot of salted water until tender. Drain well and allow to cool slightly.
Pass the potatoes through a potato ricer or alternately mash with a fork. The potatoes should be light and fluffy unlike the consistency of mashed potatoes.
Make a well in the center of the mound, add the eggs. Squeeze the excess water from the spinach, chop finely and sprinkle over the eggs and potatoes. Sprinkle salt over the ingredients.
Add 3 cups of the flour around the edges of the potato mixture.
Use a fork to lightly beat the eggs, combining them with the spinach and potatoes. Use your hands to gradually mix in the flour around the edges, using only what is needed to form a dough that is not sticky. Only if absolutely necessary, add extra flour. A dough scraper may come in handy at this point to help gather all the bits of dough. Do not over knead, the dough should be light and airy. This will take about 10 minutes.
Divide the dough into 4 pieces. On a lightly floured surface, roll the dough into a long rope of approximately 1/2 inch in diameter. Use the palms of your hands and your fingertips to exert a light pressure on the dough, rolling from the center outwards to form an even shaped rope. Use a sharp knife to cut into 1 inch pieces.
Form an indentation in the gnocchi by pressing down lightly with your thumb to roll each gnocchi on the wood board. These grooves will help the sauce adhere to the gnocchi.
Place gnocchi on a parchment covered baking sheet lightly dusted with flour to prevent from sticking. Repeat with the remaining dough.
Bring a large pot of salted water to a boil. Add gnocchi and stir. When they have all risen to the surface, drain well and add to the butter sage sauce. Serve hot topped with grated Parmigiano cheese.