Heat a large heavy-bottomed soup pot with vegetable oil, two turns of the pan, over high heat. Once you see the oil ripple, add the sliced onion, chopped garlic and sliced peppers. Season the vegetables with salt and pepper and cook, stirring frequently, for 2 minutes. Add the shredded carrots and the chicken stock. Cover with a lid and bring up to a simmer. Once simmering, add the chicken and simmer for 5 minutes, then add the noodles and simmer for 5 minutes more. Remove the soup from the heat and add the cilantro, basil and the lime juice.