Place whole russet potatoes in a large pot and cover with cold water; add a pinch of salt and bring to a boil. Cook until fork-tender, about 10–15 minutes depending on size, then drain and let cool until you can handle them.
When cool enough to touch, peel the potatoes and transfer to a large bowl. Mash thoroughly with a potato masher until smooth and free of lumps.
Turn the mashed potatoes out onto a lightly floured work surface. Make a well in the center and sprinkle about 1 to 1½ cups of the flour over the potatoes; sprinkle 1½ teaspoons salt over the flour.
Break the egg into the well and use your hands or a bench scraper to gradually incorporate the egg and flour into the potatoes until a shaggy dough forms.
Add the remaining flour as needed and knead gently (do not overwork) until you have a soft, slightly tacky dough that holds together like bread dough.
Divide the dough into portions and roll each into a long rope about ¾–1 inch in diameter. Cut the ropes into ½-inch pieces.
Optional: roll each piece over the tines of a fork to create ridges, or press lightly with your thumb to form an indentation.
Bring a large pot of salted water to a boil. Cook the gnocchi in batches for 2–3 minutes or until they float to the surface; remove with a slotted spoon.