Make the roux: Heat the canola oil in a cast-iron skillet over medium heat until hot, about 5 minutes. Whisk in both flours and cook, whisking constantly, until the roux is dark brown, about 10 minutes. Remove from the heat and let stand 10 minutes, then stir in the finely chopped onion.
Meanwhile, bring the broth and 20 cups water to a boil in a large pot. Add the roughly chopped onion, the celery and bell pepper; cook over medium-high heat, 15 minutes. Stir in the roux in 3 batches; cook, stirring occasionally, until thickened, 30 minutes. Add the cayenne, garlic powder, 2 1/2 tablespoons salt and 1/2 teaspoon black pepper. Stir in the smoked sausage and tasso. Reduce the heat to low; simmer 1 hour.
Return the mixture to a boil. Add the chicken thighs and breasts and cook 30 minutes. Remove from the heat. Skim the fat off the surface, then stir in the scallions.
Serve over rice.
Photograph by Yunhee Kim
Recipe courtesy Alcee "Butch" Bayard for Food Network Magazine