In a medium saucepan with a heavy bottom, whisk 3 tablespoons oil with 1/4 cup flour.
Cook over medium heat, whisking frequently until the mixture is a deep brown, about 15 minutes.
Add andouille, sausage, onion, green bell pepper, and celery. Cook until softened and slightly browned. (Note: if your sausage is lean, add a little oil or butter.)
Stir in garlic, Cajun seasoning, and parsley. Cook until fragrant, about 20 seconds.
Slowly stir in chicken broth making sure to scrape the fond from the bottom and sides of the pan. Simmer for 15 minutes or until the vegetables are soft and the stew is heated throughout. If the stew is too thick, add a little water.
Add okra and shrimp. Simmer until the shrimp is pink.
Serve with rice.