Bring meat to room temperature and pat dry. Season all sides with Cajun seasoning.
Heat oil in a large saucepot over high heat. Once hot, brown meat on all sides.
Remove the meat from the pot and place to the side, lower heat to medium and stir in onion, bell pepper, celery, green onions, and minced garlic.
Cook vegetables for 5-10 minutes until they begin to caramelize. Add the meat back into the pot and slowly add enough water or beef stock to cover ingredients.
Bring to a simmer, then lower heat and cook for about 3-4 hours, until fork tender, stirring occasionally and adding more liquid as needed.
Serve over hot Cajun Country Rice along with your favorite sides, like corn maque choux or smothered green beans.