Wash the potatoes thoroughly and place them in a large pot of cold water. Bring to a boil and cook until tender, about 15-20 minutes. Drain and let cool slightly.
Peel the potatoes while still warm and mash them until smooth, using a potato ricer or masher.
On a clean surface, mix the mashed potatoes, flour, olive oil, and salt. Knead until a smooth dough forms. If sticky, add a bit more flour.
Divide the dough into four parts. Roll each part into a long rope, about 1 inch thick. Cut into 1-inch pieces. Roll each piece over the tines of a fork to create ridges, or use a gnocchi rolling board if you have one.
Bring a large pot of salted water to a boil. Cook gnocchi in batches until they float to the surface, about 2-3 minutes. Remove with a slotted spoon. Serve as desired.