Place chicken stock in a 2-gallon stockpot. Place on back burner, bring to boil, and reduce to a simmer.
Mix together salt, cayenne, black pepper, cumin, paprika, and coriander and set aside.
Cut the rooster or chicken into 8 pieces, removing the backbone and discarding. Place the ham hocks in the stock to simmer.
Season the flour with salt and pepper and place in a shallow dish. Generously coat the chicken parts with some of the spice mix. Set aside the remaining spice mixture. Dust the seasoned chicken parts in the seasoned flour and set aside the remaining flour.
In a cast-iron skillet heat the chicken fat almost to smoking. Fry the chicken parts over high heat to crisp the outside, but not cook the inside of the chicken. Remove the chicken from the oil and drain on paper towels and add to stock. Keep the remaining chicken fat in the pan.
Toss andouille with a few drops of oil and place in a baking dish. Roast until fat is rendered and the surface of the andouille is caramelized, about 15 minutes. Remove and put the andouille aside.
Heat the reserved chicken fat almost to smoking. Very carefully whisk in the remaining flour. Lower the heat to medium. Whisk the flour into the roux and continue to whisk in a circular motion around the cast-iron pan. The flour will move through a range of colors from hazelnut to brick red and on to dark brown. Place 1/2 of the onions and all of the green bell peppers, garlic, and bay leaves in a large, heatproof bowl or container.
When the roux has reached a deep, red brown color, carefully pour the hot roux over the onion/pepper mixture and stir to combine.
Add the roux mixture to the stock, a few spoons at a time, leaving 5 minutes between each addition, until it is all added. Add half of the remaining seasoning mix. Allow to simmer for 30 minutes or until rooster is cooked and tender.
Strain into a large pot. Saute remaining onions and red peppers until softened and add to strained liquid. Remove meat from cooked chicken. Discard chicken bones. Add chicken pieces and andouille rounds. Place gumbo in serving bowls and finish with a spoonful of rice and sliced scallions.