In a large nonstick saucepan, heat oil over medium heat. Add white parts of the green onions, carrot and mushrooms; cook for 5 minutes, stirring occasionally. Add ginger and garlic; cook and stir for 1 minute more. Add chicken broth, water, soybeans, soy sauce and, if desired, crushed red pepper to mushroom mixture. Bring to boiling; reduce heat. Cover and simmer about 5 minutes or just until carrot is tender.