Clean all vegetables, removing bad leaves and rinsing away all the grit.
In a large pot, place all greens, onions, and garlic. Cover with water and boil for 30 minutes.
While the greens are boiling, cut all the meats and sausages into bite-sized pieces and set aside.
Strain the vegetables after boiling, reserving the liquid.
In a 12-quart stockpot place smoked sausage, ham, and brisket meats, adding 2 cups of the reserved liquid. Steam for 15 minutes.
While steaming the meats, place the chaurice in a skillet and steam until the fat is rendered. Set the chaurice aside, reserving the grease.
Purée all vegetables in a food processor or meat grinder.
Heat the skillet of chaurice grease; than add the flour, stirring constantly, for about 5 minutes, or until a light-colored roux is achieved. (The roux does not have to be brown.) Pour the roux over the steamed meats, stirring well. Add the vegetables and two quarts of the reserved liquid.
Simmer for about 20 minutes. Add the chaurice, thyme, salt, and cayenne pepper. Stir well.
Simmer for 40 minutes. Add filé powder, stir well, and remove from heat.
Serve over steamed rice.
