Place whole, unpeeled potatoes in a large pot of water and bring to a boil; cook until fork-tender, about 20–30 minutes. Drain and let cool slightly.
Cut each potato lengthwise and press the flesh through a potato ricer fitted with the finest disk onto a clean work surface; if you don't have a ricer, grate finely. Spread into an even layer and sprinkle with a pinch of sea salt.
Add about half the flour to the potatoes and gently mix, then add half the beaten egg and begin to knead lightly until combined.
Gradually add the remaining flour and the rest of the egg, kneading gently until the dough is soft but holds together; do not overwork the dough.
Divide the dough and roll each portion into a rope about 1/2 inch (1.25 cm) thick on a lightly floured surface.
Cut the ropes into 1-inch (2.5 cm) pieces, press each piece with your index finger to make an indent, and roll on a gnocchi board or the tines of a fork to create ridges.
Arrange finished gnocchi on a well-floured baking tray in a single layer to prevent sticking.
Bring a large pot of lightly salted water to a gentle boil. Cook gnocchi in batches for 1–2 minutes, or until they float to the surface, then remove with a slotted spoon.
Toss the cooked gnocchi with your preferred sauce and serve immediately.
If not cooking right away, freeze gnocchi in a single layer on a baking sheet, then transfer to freezer bags and cook from frozen when needed.
