Place the potatoes, skin on, in a large pot and fill with water to cover. Bring the water to a boil and let the potatoes cook until they are fork tender—about 45-60 minutes.
Drain the potatoes and let them cool until you can safely handle them. Peel the hot potatoes with a paring knife—the skin should easily pull off.
Using a potato masher or ricer, mash the hot potatoes and place them directly onto a large, clean work surface.
Dust the potatoes generously with flour and begin kneading them together into a dough. As you knead, continue to dust the potatoes with more flour until the dough is no longer sticky or tacky at all. At this point, stop kneading or adding flour.
As you make the gnocchi, dust the dough, pasta, work surface and tools often and liberally with more flour.
Cut a manageable chunk of dough off from the rest and roll it under your palms into a long snake, about the width of a ring finger.
Using a bench scraper or knife, cut the strand into small pieces about 1 inch (2.5cm) in length.
You can either cook these gnocchi as-is, or use a fingertip to press a hole in the center of each piece to help hold sauce.
Arrange the finished gnocchi on a clean towel dusted liberally with flour. Keep each gnocco separated so they don’t touch and stick.
Bring a large pot of water to boil and salt it generously. Gather the edges of the towel together to lift the gnocchi and pour them into the water.
Stir them very gently to prevent sticking. After cooking for just a minute or two, the gnocchi will float and rise to the surface of the water.
Skim them off with a slotted spoon and transfer into the sauce of your choice.