Place large pot on stovetop over medium-low heat. Add 1 cup unsalted butter to pot and let butter melt, moving butter around pot periodically to fully cover surface.
Once butter has melted, sprinkle 1 cup all-purpose flour into pot and whisk until flour and butter are combined into roux. Cook roux, whisking constantly, 10 to 20 minutes or until roux becomes peanut-butter brown in color.
Once desired color is achieved, increase heat under pot to medium. Add 2 cups chopped yellow onion, 1 cup chopped green bell pepper, and 1 cup chopped celery and stir to incorporate. Cook trinity, stirring frequently, 5 to 8 minutes or until softened.
When vegetables have softened, add 1 pound andouille sausage and 2 cloves garlic. Stir to incorporate, then cook 2 to 3 minutes or until garlic is fragrant. Continue stirring frequently while cooking.
While stirring, slowly pour in 6 cups low-sodium chicken broth. Stir until ingredients are fully incorporated, scraping bottom of pot if needed to loosen any aromatics that may have stuck.
Add 1 bay leaf, 2 teaspoons paprika, 1 teaspoon salt, 1 teaspoon garlic powder, 1 teaspoon onion powder, 1 teaspoon dried oregano, ½ teaspoon dried basil, and ¼ teaspoon cayenne pepper to pot. Stir to fully incorporate spices.
Increase heat under pot to medium-high and bring mixture to boil. Once liquid begins to boil, immediately reduce heat to low and simmer, uncovered, 30 minutes. Stir gumbo occasionally.
After 30 minutes, add 5 cups cooked, shredded chicken to pot. Stir to incorporate, then taste gumbo and adjust any spices as desired. Continue simmering gumbo, uncovered, 60 minutes, stirring occasionally.
After 60 minutes, divide gumbo into serving bowls. Top each bowl of gumbo with scoop of cooked white rice, garnish with sliced green onions and hot sauce if desired, and serve warm.