Thoroughly wash the potatoes, poke several times with a fork, place in a pan, cover with water, and bring to a boil.
Boil until very soft - 10-20 minutes.
Remove from water, allow to cool somewhat, and slide the skins off.
On a clean, floured surface, push the potatoes through a potato ricer or use a fork to scrape the potatoes into "flakes".
Break the egg into a bowl and whisk slightly.
Add the salt and egg and mix until very smooth and blended (should look like almost soupy mashed potatoes).
Add the flour to the potatoes. and knead until incorporated. Let rest a minute or two and add up to 2/3 cup more flour (letting it rest allows the potatoes to soak up the flour).
Knead until it feels like dough (a couple minutes).
Roll the dough into a long "snake" and cut into 1-inch pieces.
Either cook immediately or spread the gnocchi on baking sheets and freeze until time to cook.
When cooking: cook for 7-10 minutes or until the flour tastes cooked.