Place the potatoes in a pot with water to cover by a few inches. Bring to a boil over high heat. Drain and let the potatoes cool completely. Peel the potatoes, place them in a large bowl, and mash them well.

Make a large well in the middle of the mashed potatoes and pour in the eggs. Gradually pull the walls of the potato well into the eggs and mix well. Start adding the flour in small increments until the mixture can no longer absorb any more. Knead well and add two tablespoons of the oil and the salt to the dough.

Bring a pot of water to a boil while you form the dumplings and preheat the broiler.

Flour a work surface. Coat your hands with oil, take a piece of the dough, and roll it into a long strand about 3/4 inch thick. Cut the strand into 3/4-inch slices. Working in batches to avoid crowding the pot, add the slices of shlishkes to the water and cook until the dumplings rise to the surface, gently nudging them off the sides of the pot if they begin to stick. Cook for another five minutes.

While the dumplings are cooking, heat the remaining one tablespoon oil in a medium skillet over medium heat. Add the bread crumbs and toast, stirring, until browned.

Drain the shlishkes and gently toss them in the toasted bread crumbs. Transfer to a broiler pan, place under the broiler, and broil until golden brown.

Shlishkes can also be made without breading and paired with sauce instead. To freeze, roll the shlishkes in flour before boiling them and place in a zip-top bag.