Place the potatoes in a large pot and cover with cold water.
Bring to a boil over medium heat and cook for about 15 minutes, or until a fork easily pierces the potatoes.
Drain and let the potatoes cool until they are comfortable to handle, then peel them.
Mash the peeled potatoes on a clean, flat surface with a potato masher until smooth and free of large lumps.
Spread the mashed potatoes into a thin layer, sprinkle with the flour and 1/2 teaspoon salt, and use your hands to gently combine into a cohesive ball of dough without overworking it.
Divide the dough into 4 equal portions and roll each portion into a log about 1 inch in diameter.
Cut the logs into 1-inch pieces and press each piece lightly with a fork to create shallow grooves, repeating with all pieces.
Bring a large pot of salted water to a boil, add the gnocchi, and cook for 4–5 minutes or until they float to the surface.
Remove the cooked gnocchi with a slotted spoon and serve with your preferred sauce.
