Place whole, unpeeled potatoes in a large pot of cold, salted water. Bring to a boil and cook for 20–25 minutes, or until fork-tender.
Drain and let cool just enough to handle, then peel while still warm.
Use a potato ricer or mash very well with a masher until smooth and then spread the mashed potatoes out on a clean surface to cool slightly.
Sprinkle salt over the mashed potatoes and drizzle the beaten egg on top.
Add 1 ½ cups of the flour and gently mix with your hands, kneading just until a soft dough forms.
Add a little more flour if the dough is too sticky but be careful not to overwork.
Divide the dough into 4 portions.
On a floured surface, roll each portion into a rope about ¾ inch thick. Cut into ¾-inch pieces to form the gnocchi.
For the classic ridged look, gently press each piece against the back of a fork or gnocchi board and roll down.
Place shaped gnocchi on a floured tray in a single layer.
Bring a large pot of salted water to a boil.
Add gnocchi in batches; they’re done when they float to the top. Use a slotted spoon to remove and serve immediately with your favorite sauce.
