Cut potatoes into 1/2-inch cubes and carrots into 1/2-inch slices; coarsely chop onion.
Sauté vegetables in hot oil in a Dutch oven until tender.
Stir together Cheddar cheese soup and next 3 ingredients until blended; add to vegetable mixture. Bring to a boil; reduce heat, and simmer 30 minutes. Stir in 1/2 cup sliced green onions just before serving. Garnish, if desired.