Add all of the vegetables EXCEPT the garlic to browned roux and over low heat let them sweat until soft. This will cause the roux to seize up, but it's supposed to do that, and it will keep the roux from cooking much further but the vegetables will soften. Be careful not to burn the vegetables so continue to stir frequently.
Add the chicken broth and stir roux into a smooth sauce. Add garlic, bay leaf, green onions, parsley, and optional tomatoes. Taste and add salt and peppers as necessary.
Reduce heat and simmer on low heat for 1 - 2 hours. If more liquid is needed just add more broth or water. Stir occasionally to keep roux from sticking to the bottom of pot and burning. ***See Note Below!
Bring sauce back to a low boil then add sausage and chicken about 30 minutes before serving; stir gently. If you add the chicken too soon it will just fall apart. Remove from heat and serve over white rice with crusty french bread. Garnish with a few thinly sliced green onions and fresh chopped parsley. Enjoy!
***Note: At this point you can remove from the heat, let cool and put in refrigerator until you're ready to finish. When you remove it from the fridge, skim all the solid fat that has floated to the top.
You can substitute chicken for quail, rabbit, squirrel, duck or alligator! Leftovers are delicious after freezing (without the rice).
Many brands of andouille are very spicy and/or strongly flavored. If you prefer a milder brand of andouille, try Mandas or just use your favorite smoked sausage. If you prefer fresh venison or pork sausage, brown it off after the chicken is removed from pot and set aside for adding later.