Trim and discard any fat or sinew tissue on venison. Cut steak into 2-inch squares. In a small bowl, combine 1 tablespoon salt and peppers.
On a cutting board, place several pieces of venison, and sprinkle with salt mixture and flour. Using a meat mallet, pound each piece of meat until slightly flattened. Turn pieces over, and season with salt mixture and flour; pound meat again. Repeat until all meat has been seasoned and flattened.
In a large heavy stockpot, heat oil over medium heat. In batches, brown venison on both sides. Remove from pot. Add onion, bell pepper, celery, and garlic; cook, stirring frequently, until vegetables are softened, about 10 minutes.
Return meat to pot. Stir in tomatoes, beef broth, bay leaves, ¼ cup parsley, and remaining ½ teaspoon salt. Cover and bring to a boil. Reduce heat, and simmer, partially covered, stirring occasionally, until meat is tender, about 1 hour.
Remove bay leaves. Taste and adjust seasonings, if necessary. Add remaining ¼ cup parsley, and cook for 5 minutes. Serve hot over grits or rice. Garnish with green onion, if desired.
Notes
If venison is not available try substituting a lean meat, such as buffalo or grass-fed beef.
Recipe by Louisiana Cookin' at https://louisianacookin.com/venison-grillades/