Boil the peeled and quartered potatoes in a pot of salted water until they are tender when pierced with a fork.

Drain the cooked potatoes thoroughly and mash them with a potato ricer or masher until smooth.

Spread the mashed potatoes on a clean surface, allowing them to cool slightly and release steam.

Once cooled, create a well in the center of the mashed potatoes and add the flour, beaten egg, and salt.

Gently mix the ingredients with your hands until a soft, cohesive dough forms, being careful not to overwork it.

Divide the dough into several portions and roll each portion into a long rope, about 1-inch thick.

Cut the ropes into small, 1-inch pieces, then gently roll each piece over the tines of a fork to create ridges.

Bring a large pot of salted water to a rolling boil and carefully drop the gnocchi into the water in batches.

Cook the gnocchi until they float to the surface, typically 2-3 minutes, indicating they are done.

Remove the cooked gnocchi with a slotted spoon and serve immediately with your favorite sauce, such as pesto or marinara.