Cut meat into serving-size pieces; sprinkle with salt and pepper.
Pour 1/2 cup oil into a Dutch oven. Fry steak in batches in hot oil over medium-high heat until browned (about 2 minutes on each side.) Remove to platter, and repeat until all meat is browned.
Measure pan drippings; add enough oil to drippings to measure 2/3 cup, and return to Dutch oven. Add flour; cook over medium heat, whisking constantly, 10 minutes or until roux is caramel colored.
Stir in onion and next 5 ingredients; cook until tender. Stir in tomatoes and next 3 ingredients, stirring well.
Return meat to Dutch oven. Bring to a boil; cover, reduce heat, and simmer 1 1/2 hours, stirring occasionally. Remove and discard bay leaves. Serve with Baked Cheese Grits.