Add salt, egg and flour to potatoes and mix well. Dough should not be thin. More or less flour may be used according to size of potatoes.
Put dough on plate. Use a teaspoon to scrape off small portions at a time and place in boiling water. Boil about 15 minutes. Keep stirring to prevent scorching. Drain in colander. Rinse once with water. Don't let Halushki get too cold, place in bowl.
Brown onion in shortening, add cabbage and fry slowly until browned, about 20 minutes. Pour over Halushki, mix well (salt to taste) and serve hot.