Cut the meat into 3-inch squares. Season with salt and pepper, then dredge in the flour and shake off excess. Heat 2 tablespoons of the cooking oil in a heavy skillet, brown the meat lightly and drain on paper towels.
Make a roux in the skillet with 2 tablespoons of flour and the remaining oil, browning until it's a rich dark color. Add all other ingredients (except the grits) to the roux and simmer until the mixture thickens, about 15 minutes. Return the meat to the pan, cover the skillet and cook until tender, about 1 hour. Stir often. Serve the grillades and sauce with hot grits.