Prep - Slice sausage into ½-inch disks. Cut ham into ½-inch dice. Rinse and drain rice a few times. Chop all vegetables, either by hand or in a food processor. Measure out beef or chicken stock.
Make Base - In a large pot, add oil and cook sausage slices over medium-high heat until browned, a few minutes. Diced ham is added next and cooked for about 3 minutes. Stir in onions, green peppers, garlic and celery. Cook until soft, about 5 more minutes. Add all the spices, bay leaves, and diced tomatoes with liquid. Cook a few minutes and then add stock and simmer for 30 minutes over medium heat..
Cook Jambalaya - Add rice and bring to a boil. Cook for 3 minutes. Cover pot and reduce the heat to very low. After 15 minutes, remove cover, and stir. If using shrimp, add now. Return cover and cook for another 15 minutes. Stir in scallion, cover, and cook 5 minutes more. Rest jambalaya off the heat for 5 minutes with a kitchen towel between the pot and cover. Remove cover and towel, adjust salt. Fluff-up rice with a fork and serve in bowls with warm crusty French bread and Tabasco or Crystal hot sauce on the side.