Brown meat, drain, and set aside. In the same pan, sauté onion. Add ginger and garlic when onions are translucent, after about 3 to 5 minutes. Cook for 2 minutes. Add remaining ingredients, except greens of green onions. Simmer all for 3 minutes. Add meat and cook about 3 to 5 minutes more.
Just before serving, mix in remaining green onions. Serve on lettuce leaves with grated carrots and cilantro leaves (if desired).