Combine flour and cajun seasoning in a large plastic bag. Add steak and shake to coat evenly.
Heat 2 tablespoons of oil in a cast iron Dutch oven or a deep pan set over medium-high heat.
Add steak and brown on both sides. Remove from pan and set aside.
Add remaining oil to pan along with celery, onion , green pepper, and red pepper. Cook until soft, stirring occasionally, about 5 minutes.
Add garlic and cook for 1 minute.
Sprinkle 1 tablespoon flour over the veggies and stir to mix it in well.
Gradually stir in the beef broth and then add the can of tomatoes.
Add bay leaves, Worcestershire sauce, red wine vinegar, Tabasco sauce, and Italian seasoning.
Add steak back to pan, cover and simmer for 1 hour..
Meanwhile make grits. To make grits, bring water, milk, and salt to a boil in a medium saucepan.
Gradually whisk in grits so that they do not clump. Turn heat to low and cook according to package directions (probably a good 45 minutes for stone-ground or shorter for quick grits.) Stir frequently to prevent the grits from scorching on the bottom of the pan. If grits are getting too thick, you can add more water.
Once done, turn heat off and stir in butter, cheeses, and white pepper. Keep warm.