Heat the vegetable oil in a large pot over medium heat. Gradually whisk in the all-purpose flour.
Stir it continuously for about 15-20 minutes until it turns a dark brown color, like milk chocolate. This step takes time and patience—don't be tempted to increase the heat to speed up the process because it could end up burning.
To Make The Gumbo:
Add the green bell pepper, onion, and garlic to the pot with the roux and stir well. Cook the vegetables for 5-7 minutes until tender. Season with the Cajun seasoning. Meanwhile, cut the andouille sausage into ¼-inch thick slices.
Pour in 4 cups of chicken broth, then add the sliced sausage and the deboned rotisserie chicken.
Bring the gumbo to a boil, lower the heat to medium-low, and let it simmer for about 1 hour. In the meantime, you can peel and devein the shrimp.
After the gumbo has been simmering, add the peeled shrimp and half of the chopped parsley. Cook for another 10 minutes.
Taste the gumbo and adjust with additional salt, pepper, or Cajun seasoning if needed.
Serve it hot over cooked white rice with some fresh parsley on top.