Rinse the potatoes and scrub the skins with a vegetable brush.
Place the potatoes in a large pot (6 quarts) and add enough cold water to cover them by two inches. Place over high heat on the stove, add a tablespoon of salt and cover with a lid.
When the water starts boiling, lower the heat slightly so the pot doesn't boil over. Keep the pot covered and let it simmer until the potatoes are tender and you can stick a fork in them. Mine take 25 minutes, but check the potatoes a bit sooner.
When the potatoes are done, turn off the heat and drain them in a colander in the sink. Let them sit until cool enough to peel off the skin, but still warm. Peel the potatoes and discard the skin.
On a clean surface, add two cups of flour and ¼ teaspoon salt. Stir with a fork to combine. Make a well in the center.
While still warm, cut each potato in half the short way so that it can fit into your ricer. Place a potato half into the ricer, and while holding it over the flour mixture, squeeze the handles until strands of potatoes fall into the flour. If needed, scrape inside the ricer if it seems stuck, and squeeze again. Continue ricing the remaining potatoes into the flour mixture.
Mix the dough with your hands, incorporating the flour into the potatoes. If the dough is too sticky, add an extra couple of tablespoons of flour at a time just until the dough comes together. Knead the dough just until it's smooth and soft. (Do this by folding it over and then pressing down with the bottoms of your palms. Rotate the dough and fold and press again. Continue until it's smooth.)
Form the Gnocchi
Shape the dough into a ball. Use a dough cutter or smooth knife to cut off a small section of dough. Rub the section of dough between your palms until it forms a log, then roll it on a floured surface with your fingertips into a rope about the width of a finger (no more than ¾-inch thick.) Cut the rope into 1-inch pieces. (See the process photos in the post.)
If you want to make grooves on the gnocchi, roll each piece on a floured gnocchi board or the back of a fork with your thumb while slightly pressing down. An opening will form underneath the gnoccho.
Place the gnocchi in a floured sheet pan and let them rest for 20 minutes to dry.
Boil the Gnocchi
Rinse the pot you used to cook the potatoes and wipe it clean. Fill the pot about ⅔ full with cold water. Place it on the stove over high heat and add a tablespoon of salt. Cover the pot and let the water come to a boil.
When the water is boiling, use a bench scraper or slotted spoon to transfer half of the gnocchi to the pot. Stir briefly so they don't stick. After about a minute, the gnocchi will float on the surface and should be done, but taste one to be sure it's cooked through. Remove the cooked gnocchi with a slotted spoon and place them in a pan of prepared sauce or add them to a 9x13 pan and mix warmed sauce into them. Cook the rest of the gnocchi as before.
Store leftover boiled gnocchi in a sealed container in the refrigerator for up to four days. See notes for storing uncooked gnocchi.
Notes
Don't use waxy potatoes like red ones, because they contain too much moisture and can make the gnocchi turn out gummy.
Use just enough flour to make the dough come together, so the gnocchi doesn't turn out dense.
Some people add a beaten egg to the gnocchi dough to make it easier to mix. We prefer the lighter gnocchi we get without using an egg. If you're having trouble getting the dough to come together, you can add one beaten egg. The gnocchi will be a bit denser and not have as much potato flavor.
Uncooked gnocchi can stay in the refrigerator for just one or two days. They need to be cooked or frozen by then, because they'll become sticky and damp and can lose their shape. Keep them on a floured sheet pan, dusted with more flour and cover them loosely with a lint-free towel.
It's best to freeze homemade gnocchi without cooking them first. Place uncooked potato gnocchi on a floured sheet pan in a single layer, covered with wax paper. Freeze for at least an hour, then transfer them to a zip-top plastic freezer bag and use them within three months.
To cook frozen gnocchi: Add them to boiling, salted water and wait for them to float before scooping them out with a slotted spoon. They'll take about five minutes to cook.