Boil the potatoes, skins on, in salted water for around 30-40 mins, depending on size. They should be tender all the way through, but not splitting. Drain.
Allow the potatoes to cool for about 20 minutes, then peel. While still warm, push the potatoes through a potato ricer or fine sieve onto a work surface.
Make a well with the potatoes. Pour on about 3/4 of the flour and the salt.
Crack the egg into the center. Lightly whisk the egg with a fork. Then use the fork to begin to incorporate the potato, egg and flour.
Once mostly incorporated, use your hands to bring the ingredients together to form a ball. You want the ingredients to be mixed, but without overworking the dough. Overworked will lead to rubbery gnocchi.
Divide the dough into 4 small balls. Use some of the remaining flour to dust the work surface. Roll each ball of dough on a floured surface to form a long, even log.
With a knife or pastry cutter, cut the log into bite-sized pieces. Store them on a floured surface until ready to cook, or transfer them to the freezer.
To cook, gently boil in salted water for roughly 3 minutes or until they float to the surface. Do not overcook. Drain. Mix with sauce. Serve.