Add the potatoes to a large pot and cover with water. Bring to a boil and cook until the potatoes are just fork tender, about 20 to 25 minutes. Drain and allow to cool.
When the potatoes are cool enough to handle, peel the skin. Cut the potatoes into thirds and then press through a potato ricer over a lightly floured surface. If you don't have a potato ricer, you can grate them or mash them.
Sprinkle the flour and salt over the top of the potatoes. Make a well, and add the egg. Use a fork to gently bring everything together, and then gently work into a dough, being careful not to over knead, as that will make the gnocchi tough. Form into a ball.
Cut the ball into 8 pieces. Roll each of the pieces into a ¾" thick log, then cut the log into 1" pieces. If desired, roll the pieces over the tines of a fork or a gnocchi board to give it ridges. (If freezing or saving for later, do so at this point).
Bring a pot of salted water to a boil. Working in batch so as not to overcrowd the gnocchi and cause it to stick to each other, add the gnocchi to the boiling water and cook until they float to the top, about 2 to 3 minutes. Remove with a slotted spoon and serve with your desired topping or sauce.
Notes
Serves 8 as a side dish or 4 as a main course. Calories are automatically generated. For best results calculate based on your exact ingredients.