Place the potatoes in a large pot of salted water and bring to a boil.
Cook until the potatoes are tender, about 20-25 minutes.
Drain and let the potatoes cool slightly, then peel them.
Pass the peeled potatoes through a potato ricer or mash them until smooth. Spread the mashed potatoes out on a clean surface and let them cool completely.
Sprinkle the cooled mashed potatoes with the flour and salt.
Make a well in the center and add the beaten egg.
Using your hands, gently mix the ingredients together until a dough forms. Be careful not to overwork the dough.
Lightly dust your work surface with flour.
Divide the dough into 4 portions and roll each portion into a long rope, about 1/2 inch (1.25 cm) in diameter.
Cut the ropes into 1-inch (2.5 cm) pieces.
If desired, you can roll each piece over the tines of a fork to create ridges.
Bring a large pot of salted water to a boil.
Add the gnocchi in batches and cook until they float to the surface, about 2-3 minutes.
Use a slotted spoon to remove the gnocchi and transfer them to a plate.
Enjoy your meal!