Heat olive oil in a large pot over medium-high heat. Add cabbage and onion; saute until lightly browned and translucent, 6 to 8 minutes. Add carrots, mushrooms, and garlic; saute until tender, about 3 minutes. Add broth, potsticker sauce, sherry, ham, ginger, orange peel, and pepper. Increase heat to high; bring soup to a boil.
Reduce heat to medium; cook until flavors meld, about 15 minutes. Remove and discard orange peel. Add potstickers; cook, covered, until tender, about 10 minutes. Stir in cilantro.