Heat the oil in a large cast-iron Dutch oven over medium heat. Add the sausage and cook until it start to render the fat. Add the onions, bell peppers, 1 teaspoon of the salt, the Creole seasoning, and ½ teaspoon of the cayenne. Stirring often, brown the vegetables and sausage until they are caramelized, about 15 minutes. Scrape the bottom and sides of the pot to loosen any browned particles (fond). Add the garlic and cook for 1 minute.
Season the chicken with the remaining 1 teaspoon salt and remaining ½ teaspoon cayenne. Add the chicken, ham, and the bay leaves to the pot. Brown the chicken for 8 minutes, scraping the bottom of the pot to loosen any browned bits.
Add the rice and stir for 2 to 3 minutes to coat evenly. Add the water, stir to combine, and cover. Cook over medium heat for 30 to 35 minutes, without stirring, or until the rice is tender and the liquid has been absorbed.
Lay the shrimp on top of the cooked rice during the last 5 minutes of cooking and steam until just pink. Remove the pot from the heat and let stand, covered, for 2 to 3 minutes. Remove the bay leaves. Stir in the green onions and parsley, and serve.