Make the roux: Melt butter in a large Dutch oven over medium-low heat. Sprinkle flour over top and stir constantly until the mixture turns a deep golden color, like peanut butter or dark caramel, about 15 minutes. Watch carefully and stir constantly to prevent burning. For an even bolder flavor, continue cooking and stirring the roux until it reaches a deeper chocolate color (optional).
Cook the vegetables: Add onion, bell pepper, and celery to the pot. Increase heat to medium and cook, stirring often, until softened, about 5 minutes.
Stir in garlic and sausage and cook for 1 more minute.
Add the liquids: Whisk in the chicken broth gradually until smooth.
Add the diced tomatoes with their juices. Increase heat and bring to a boil.
Simmer: Reduce heat to low. Stir in thyme, oregano, bay leaf, paprika, and cayenne. Simmer uncovered for 30 minutes, stirring occasionally.
Add chicken and okra: Stir in the shredded chicken and okra. Return to a simmer and cook for 10 more minutes. Remove bay leaf.
Finish: Remove pot from heat. Stir in green onions, parsley, and filé powder. Taste and season with salt and additional cayenne if desired.
Serve: Ladle into bowls and top each serving with a scoop of warm rice.