In a large, heavy bottom stock pot combine flour and oil. Cook on medium-low heat, stirring constantly for 30-45 minutes until it becomes dark brown.
In a separate skillet on medium-high heat place the sausage slices in one layer in the pan. Brown them well on one side (2-3 minutes) and then flip each over to brown the other side.
Add ½ cup of the chicken broth to the hot skillet that had the sausage to deglaze the pan. Pour the broth and drippings into your large soup pot.
Add remaining 5 ½ cups of chicken broth. Add veggies, parsley, garlic and roux to the pot and stir well.
Bring to a boil over medium heat and boil for 5-7 minutes, or until the vegetables are slightly tender. Skim off any foam that may rise to the top of the pot. Stir in cajun seasoning, to taste.
Add chicken, sausage, and shrimp. Taste and add more seasonings to your liking until you reach the perfect flavor. Serve warm over rice.