First, let's make the roux which is the backbone of this gumbo. Heat the 1/4 cup vegetable oil in a large pot over medium heat. Gradually whisk in the 1/2 cup all-purpose flour.
Stir it continuously for about 10-15 minutes until it turns a dark brown color like milk chocolate. This step takes time and patience, so be careful not to increase the heat to speed the process because it could end up burning.
Add the vegetables 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 1/4-inch thick slices.
Pour in 4 cups of chicken broth, add the sliced sausage and the meat from 1/2 rotisserie chicken.
Bring the gumbo to a boil, lower the heat and let it simmer for about an hour. In the meantime, you can peel and devein the 1 cup of shrimp if they aren't already.
After the gumbo has been simmering, add the 1 cup shrimp and 1/2 bunch of fresh 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.