Heat the vegetable oil and sesame oil in a large pot over medium heat. Add the onion, garlic, and bell pepper and saute until softened. Add the rest of the carrots, green beans, the ginger, salt and pepper and continue to cook a few minutes until the carrots and green beans just begin to soften.

Pour in the broth, soy sauce, and water and stir to combine. Cover the pot, bring the broth to a boil, then turn the heat down to low. Continue to simmer until the carrots are soft and easily pierced. Add the dried noodles to the pot and continue to simmer until the noodles are cooked through, according to the package directions. Serve soup immediately topped with chopped green onions, chives, or other herbs.