Make the Roux: In a large, heavy bottom stock pot combine flour and oil. Cook on medium-low heat, stirring constantly for 30-45 minutes until dark as chocolate with a soft, 'cookie dough' like consistency.
Brown the sausage in a separate skillet on medium-high heat, 2-3 minutes per side. Remove to a plate.
Add ½ cup chicken broth to the hot skillet to deglaze. Pour into soup pot with remaining broth, vegetables, parsley, garlic and roux. Bring to boil for 5-7 minutes.
Stir in cajun seasoning, then add chicken, sausage, and shrimp.
Adjust seasonings to taste and serve warm over rice.