Place the potatoes in a large pot and cover with cold water. Boil until fork-tender, about 25 to 35 minutes depending on the size of the potatoes.
Drain the potatoes well, then peel them while they are still warm.
Mash the potatoes until very smooth. For the lightest texture, use a potato ricer if you have one.
Let the mashed potatoes sit for a few minutes so the steam can escape and the potatoes are not too wet.
Transfer the potatoes to a lightly floured surface. Add the egg, salt, and 1 1/2 cups flour.
Gently mix until a soft potato dough forms. Add more flour only if the dough feels too sticky to handle.
Divide the dough into smaller pieces and roll each piece into a long rope, about 3/4 inch thick.
Cut the ropes into small gnocchi pieces, about 1 inch long.
Lightly dust a fork with flour, then gently roll each piece over the back of the fork to create ridges.
Place the shaped gnocchi on a lightly floured tray in a single layer.
To cook, boil the gnocchi in salted water until they float to the top, then cook for 30 to 60 seconds more. Remove with a slotted spoon and serve with your favorite sauce.