Heat 2 tablespoons of oil in large soup pot over medium heat. Scatter 1/4 teaspoon of salt and 1/4 teaspoon of pepper over the turkey. Add to a hot pan and cook until the turkey is no longer pink in the center, 5 to 10 minutes, turning once or twice. Remove to cutting board. When cool, shred with a fork.
Add 2 teaspoons oil to the pot. When hot, add the okra and cook until tender, about 5 minutes. Add onion, pepper, celery, and garlic. Cook until all the vegetables are tender, about 10 more minutes, stirring a few times. Transfer the vegetables to a bowl.
Add remaining 1/2 cup oil to pot. Gradually whisk in flour. Reduce heat a little and cook, whisking frequently, until mixture (the roux) stars to thicken and turns medium brown, about 8 minutes. Watch carefully to avoid burning the roux. It should be a nutty dark-brown color. If it burns, clean the pot and start over again with fresh oil and flour. Gradually whisk in 3 cups of the broth. Stir in reserved turkey and vegetables, tomatoes, sausage, bay leaves, cayenne, remaining 1/2 teaspoon salt, and remaining 1/2 teaspoon pepper. Bring to boil over high heat. Reduce heat to medium-low and low simmer gently, uncovered, for 45 minutes.
Stir in shrimp and cook until bright pink, about 5 minutes. Taste and add more salt and pepper as necessary. Remove bay leaf before serving. Garnish with scallions and parsley, if using. Serve with slices of a Panera Bread French Baguette.
Tip: If you can’t find andouille sausage, use another spicy smoked sausage, chorizo, or kielbasa. Or use tasso ham.