Combine the flour and oil in a cast iron skillet and cook over medium heat, stirring constantly, until a roux is formed that is the color of peanut butter. Transfer roux to a small bowl and set aside. In the same skillet, cook the ground beef and pork over medium-high heat until well browned, about 8 to 10 minutes. Add the onions, bell peppers, celery, Essence, 1/2 teaspoon of the salt, 1/4 teaspoon of the black pepper and the cayenne pepper and cook until the vegetables are softened, about 4 minutes. Add the garlic and cook for 1 minute. Add the roux mixture and 1 1/2 cups water and stir well to combine. Bring to a boil, then reduce heat to a simmer and cook for 10 minutes. Set aside to cool to room temperature. Add the crumbled cornbread, green onions and parsley, and stir well to combine.
Preheat the broiler to high.
Using a sharp, thin knife, cut a pocket in the brisket from the thin side of the meat. Be careful not to pierce the 3 sides, the top or the bottom. Season the meat on both sides as well as inside the pocket with the remaining 2 teaspoons of salt and 1 1/4 teaspoons of black pepper. Carefully stuff the brisket with the meat and cornbread mixture, reserving 2/3 cup of the stuffing on the side. Using a large trussing needle and cotton string, carefully sew the open side of the brisket. Rub the brisket on both sides with the vegetable oil. Place brisket in a Dutch oven or roasting pan just large enough to hold the brisket and broil until golden brown on both sides, about 15 minutes. Add the beers and the reserved meat stuffing to the Dutch oven and cover the pan.
Reduce the oven temperature to 300 degrees F and cook the brisket for 2 hours. Uncover the pan and carefully turn the brisket. Bake the brisket, covered, for 2 hours longer, or until the brisket is very tender.
Remove the brisket from Dutch oven and set aside, lightly covered with foil, to rest for 15 to 20 minutes before serving. (Brisket will carve more easily when cooled.) Place the Dutch oven on the stovetop and cook the drippings until reduced to a gravy consistency. (Depending on how airtight your pan is, you might not need to reduce the cooking liquid at all.)
Serve the brisket with the pan juices.
Yield: 10 to 12 servings