Clean all vegetables in running water, making sure to pick out bad leaves, heavy stems, and grit. Cover with three gallons of water and boil for 30 minutes. Drain the vegetables but save the water. Chop all the vegetables fine.
Cut sausages into bite-size pieces. Put them and the brisket into a kettle with two cups reserved vegetable stock. Bring to a light boil for 15 minutes.
Cook the chaurice in a skillet until all the fat has been cooked out. Remove the chaurice and drain. Stir in the flour and cook over medium heat for five minutes, stirring constantly, to make a light brown roux. (Add a little vegetable oil if necessary.) Stir in enough vegetable stock to dissolve the roux, and add the pan contents to the kettle.
Add vegetables and about a gallon of the reserved vegetable stock. Simmer for 20 minutes.
Add chaurice, thyme, salt, and cayenne pepper; stir well. Simmer for 40 minutes more. Stir in filé powder, then remove from heat. Adjust seasonings, and serve in bowls over rice.
