Wash and scrub the potatoes but do not peel. Place the whole potatoes into a large pot and cover with plenty of water. Turn the heat on to high and bring the water to a boil then turn down the heat and simmer until the potatoes are fully cooked. This will take about 25 to 30 minutes. Check that the potatoes are cooked all the way through by poking with a paring knife.
Carefully drain the potatoes or use a pair of tongs to lift the potatoes out of the water and set aside on a plate. Let cool for 5 to 10 minutes.
Use a paring knife or spoon to carefully peel the warm potatoes. Try to remove just the skin and save as much of the flesh as possible. Cut the potatoes in half and pass through a ricer to mash. If you don't have a ricer then use a potato masher to mash the potatoes as finely as possible.
Turn the mashed potato onto a clean counter and make a hole in the centre. Crack the egg into the centre of the potatoes and use a fork to lightly beat the egg. Work the beaten egg into the mashed potatoes and roughly mix together.
Sprinkle the flour over top of the potatoes along with the kosher salt. Use a bench cutter or a spatula to start cutting the flour into the potato mixture. Once the flour is partially mixed switch to using your hands to work the flour into the dough. Knead lightly until the dough forms a smooth ball.
Cut the dough into quarters. Cover the pieces you aren't using with a towel or cling film. Lightly flour the dough you are going to be shaping. Start rolling the dough into a long rope. Continue to roll the rope of dough until it is a ½ inch in diameter.
Using the bench cutter or a kinfe cut the rope of dough into small ½ inch pieces. Lightly dust the gnocchi with flour and gently roll the pieces around on the counter or between your hands to smooth the edges and cover with flour. This will help the gnocchi not stick together. Transfer the gnocchi to a parchment lined baking sheet, spreading them out so they aren't touching.
If not using right away transfer the baking sheet to a freezer until the gnocchi are frozen. Transfer the frozen gnocchi to a freezer bag and store in the freezer. The gnocchi can be stored in the freezer for several months.
To cook the gnocchi, bring a large pot of salted water to a boil. Add the fresh or frozen gnocchi all at once. Gently stir with a wooden spoon to prevent the gnocchi from sticking or clumping together. Continue to cook, stirring occasionally, until the gnocchi begin to float. Cook for another minute. Use a slotted spoon to remove the gnocchi from the water or carefully drain in a colander. Finish the gnocchi by adding your favourite sauce!