My grandma's vegetable soup has always been a family favorite. My mother frequently served it on Friday when we weren't allowed to eat meat. The egg dumplings are a must! Very firm, not the usual soft variety. With the browned butter, this is not a low fat recipe but so delicious! You can reduce the fat content by using condensed milk instead of 1/2 & 1/2. If we won't be eating the entire recipe, I don't add the cream or milk to the pot but add a little to each bowl just before serving. Then I freeze the remaining soup for another meal. Can be stored in freezer for several months.
Saute onion in 3-4 quart kettle until soft tender and just beginning to brown. Meanwhile, prepare potatoes and carrots and add to kettle, along with water and seasonings, after oninon is cooked. Bring to boil, reduce heat and simmer uncovered for about 1/2 hr. Add green beans, peas and broth to replace the liquid that has evaporated. Stir in 1/2 & 1/2 or evaporated milk just before serving.
In 2-3 quart kettle, bring salted water (good tsp or more) to boil. Beat egg, milk and 1/2 tsp salt with fork. Add some of the flour and all of the cornstarch. Mix and continue adding flour until until dough begins to pull away from sides of bowl and forms a soft, sticky ball.
Drop dough by good tablespoon full into boiling water. It helps to dip the spoon into boiling water first so that sticky dough drops more easily from the spoon. Reduce heat and simmer, covered, for 20 minutes. Drain dumplings in colander and transfer to serving bowl. Drizzle browned butter over dumplings. Serve with soup.