Add the beef to a large mixing bowl. Season with the Cajun seasoning and salt and pepper to taste, tossing to coat well. Add the flour and toss to coat the meat completely. Turn the meat out onto a well-floured surface and lightly pound the meat with a meat mallet. Turn the meat over and lightly pound the other sides of the meat.
Heat 1/4 cup of the oil in a large cast-iron pot over medium-high heat. When the oil is hot, add the meat, in batches and brown evenly on both sides, for 5 to 6 minutes. (Add additional oil if needed.) Set aside the browned beef.
When beef is finished, drain all but about 3 tablespoons of the oil. Add the onions, bell peppers, and celery to the oil. Season with salt (about a 1/2 teaspoon) and the cayenne. Stir, scraping the bottom and sides of the pot to loosen any browned particles. Cook for 5 to 6 minutes, or until the vegetables are wilted. Add the tomatoes and garlic. Cook, stirring often and scraping the bottom and sides of the pot for 3 to 4 minutes.
Add the bay leaves, thyme, oregano, basil, stock, and wine. Return the browned meat to the pot and season with the remaining 1/2 teaspoon of salt, and 1/4 teaspoon of black pepper.
Bring the liquid to a simmer, cover partially, and reduce the heat to low. Cook for about 1 3/4 to 2 hours, stirring occasionally, or until the meat is very tender. Taste for seasoning and adjust as needed. Remove the bay leaves and stir in the chopped parsley. Garnish with some chopped green onions and serve immediately over grits.
Keywords: Bargain Meal of the Week, Beef, Bell Peppers, Cajun & Creole, canned tomatoes, emeril lagasse, Grits, Round Steak, Tomatoes