Instructions

Pat a 3-pound chicken dry inside and out with paper towels. Heat 2 tablespoons oil in 7-quart or larger Dutch oven over medium-high heat until just smoking. Add chicken and cook, turning as needed, until well browned on all sides, 10 to 12 minutes. Add 12 cups chicken broth, 2 ham hocks, 1 halved onion, reserved shrimp shells from 1½ pounds large shrimp, 6 smashed garlic cloves, and 2 bay leaves and bring to simmer over high heat. Reduce heat to low; cover; and simmer until chicken registers at least 160 degrees in breasts and thighs, 40 to 45 minutes.
Off heat, transfer chicken to cutting board and let cool slightly. Pull meat from bones, shred into bite-size pieces with 2 forks, and transfer to bowl; refrigerate meat while finishing stock. Add skin and bones to stock and bring to simmer over medium-high heat. Reduce heat to medium-low; cover; and simmer until ham hocks are tender, 1 to 1½ hours.
Off heat, transfer ham hocks to cutting board and let cool slightly. Strain stock through fine-mesh strainer set over large bowl or container (you should have about 12 cups stock; add water as needed to make up difference). Shred ham hocks into bite-size pieces and transfer to bowl with chicken meat (keep refrigerated); discard skin and bones. Skim excess fat from surface of stock using large spoon or ladle; set aside. (Cooled stock and shredded meats can be refrigerated separately for up to 3 days or frozen for up to 1 month; thaw before using.)
Heat remaining 1¼ cups oil in now-empty, dry Dutch oven over medium-high heat until just smoking. Add 1½ cups all-purpose flour and cook, whisking constantly, until roux is color of milk chocolate, 8 to 14 minutes. (Roux will begin to smoke during final few minutes of cooking.) Reduce heat to medium and add 2 seeded and chopped green bell peppers, 3 chopped celery ribs, 1 tablespoon sugar, 1 tablespoon Creole seasoning, and 2 chopped onions. Cook, stirring and scraping bottom of pot often, until vegetables are softened, about 10 minutes.
Stir in 2½ teaspoons pepper, 1 teaspoon smoked paprika, 1 teaspoon white pepper, and 10 minced garlic cloves and cook until fragrant, about 2 minutes. Add reserved stock; 1 pound andouille sausage, quartered lengthwise and sliced ½ inch thick; 12 thyme sprigs; and remaining 2 bay leaves, scraping up any browned bits. Bring to simmer over medium-high heat. Cover, reduce heat to low, and simmer for 1 hour.
Meanwhile, cook 1 pound smoked sausage, sliced ¼ inch thick, in 12-inch nonstick skillet over medium-high heat until browned, 7 to 10 minutes. Using slotted spoon, transfer sausage to plate; set aside.
Add 12 ounces okra, trimmed and cut into ½-inch pieces; shredded chicken and ham; and browned sausage to gumbo and cook, covered, until okra is tender, 20 to 25 minutes. Add 1½ pounds shrimp, peeled, deveined, and tails removed, and cook, uncovered, until opaque, about 5 minutes. Off heat, skim excess fat from surface of gumbo. Discard bay leaves and thyme sprigs. Season with salt and pepper to taste. Serve over cooked white rice, sprinkled with 8 thinly sliced scallions.