Bring a large pot of salted water to a boil. Cook potatoes in boiling water until tender but still firm, about 15 minutes. Drain, cool slightly, and peel.

Mash potatoes with a fork, masher, or ricer; place in a large bowl and season with salt. Stir in beaten egg and olive oil. Knead in enough flour to make a soft dough.

Roll dough into a long rope on a floured work surface. Cut the rope into 1/2-inch pieces.

Bring a large pot of lightly salted water to a boil. Drop in dough pieces and cook in boiling water until gnocchi float to the top, 3 to 5 minutes. Remove with a slotted spoon to a serving plate.

Serve gnocchi with hot pasta sauce.