Add onion to the pot and stir. If you have good knife skills, you don't need to pre-chop any of the vegetables. Just keep a quick pace and add the garlic, green pepper, carrots, corn, tomato, jalapeño, and beans one-by-one to a large pot over medium heat. Cover with chicken broth let simmer for about 5-7 minutes, stirring. Chop the sausage into half-inch pieces and add to the pot with green beans. Cover and continue to simmer, stirring (and tasting) occasionally, until the green beans are tender, about 8-10 minutes. Remove corn cobs and season to taste with salt and pepper. Ladle into bowls and garnish with basil.