Simmer potatoes in salted water until fork tender, about 20 minutes. Drain and let steam dry for 5 minutes. Peel.
Rice potatoes into a bowl while still hot. Let cool completely.
Stir flour and salt into potatoes until combined. Make a well and add egg. Mix until a dough forms, adding flour as needed.
On a floured surface, divide dough into 4 pieces. Gently roll each into a 3/4 inch thick rope.
Cut ropes into 3/4 inch pillow-shaped dumplings using a knife or bench scraper.
In a large pot, bring salted water to a boil. Working in batches, add gnocchi and stir gently to prevent sticking. Cook 2-3 minutes until gnocchi float to the top.
Remove cooked gnocchi with a slotted spoon to a lightly floured tray to prevent sticking. Cool and serve with your favorite sauce. Enjoy!
