Heat a large heavy-bottomed soup pot with vegetable oil, 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 1 cup shredded carrot and 6 cups chicken stock or broth. Cover with a lid and bring up to a simmer. Once simmering, add the basil and chicken simmer 5 minutes then add noodles and simmer 5 minutes more. Remove the soup from the heat and add the sesame and hot chili oil and the juice of 1 lime.