Fill a large pot with cold water. Salt the water, then cut potatoes in half and place them in the pot. Bring the water to a boil and cook the potatoes until tender throughout, this takes roughly 40-50 minutes.
Remove the potatoes from the water. Place each potato piece on a large cutting board and peel each potato as soon as possible after removing from the water. Save the potato water.
Let the potatoes cool spread out across the cutting board. Long enough that the egg won’t cook when it is incorporated into the potatoes. Mash them through a potato ricer or a food mill using the disk with the smallest holes. When you are ready, pull the potatoes into a soft mound – drizzle with the beaten egg and sprinkle 3/4 cup of the flour across the top. Scrape underneath and fold, scrape and fold until the mixture is a light crumble. Very gently. This is also the point you can add more flour (a sprinkle at a time) if the dough is too soft and is sticking to your hands. I usually end up using most of the remaining 1/4 cup flour, but it all depends on the the flour, and potatoes. The dough should be moist but not sticky. Cut it into 8 pieces. Now gently roll each 1/8th of dough into a snake-shaped log, roughly the thickness of your thumb. Use a knife to cut pieces every 3/4-inch (see photo). Dust with a bit more flour.
To shape the gnocchi hold a fork. Use your thumb and press in and down the length of the fork. The gnocchi should curl into a slight “C” shape, their backs will capture the impression of the tines as tiny ridges (good for catching sauce later). Set each gnocchi aside, dust with a bit more flour if needed, until you are ready to boil them. This step takes some practice, don’t get discouraged, once you get the hang of it it’s easy.
Now that you are on the final stretch, either reheat your potato water or start with a fresh pot (salted), and bring to a boil. Cook the gnocchi in batches by dropping them into the boiling water roughly twenty at a time. They will let you know when they are cooked because they will pop back up to the top. Fish them out of the water a few at a time with a slotted spoon ten seconds or so after they’ve surfaced. Have a large platter ready with a generous swirl of whatever sauce or favorite pesto you’ll be serving on the gnocchi. Place the gnocchi on the platter. Continue cooking in batches until all the gnocchi are done. Serve immediately, with a drizzle of good olive oil and fresh pepper on top or with any pasta friendly sauce. Serves 4. Yummy!
*In Italy usually gnocchis are part of your side dish or appetizer. I like them best with a meat sauce but they are delicious just with some olive oil, salt and pepper