Pat the alligator meat dry. Season it with ½ teaspoon salt, black pepper, and Cajun seasoning.

Heat 1 tablespoon oil in a large Dutch oven or heavy pot over medium-high heat. Brown the alligator in batches for 2–3 minutes per batch. Transfer it to a plate. Add the remaining tablespoon of oil as needed.

Reduce the heat to medium-low. Add ¼ cup oil or butter, then whisk in the flour. Cook, stirring constantly, for 8–12 minutes, until the roux is the color of peanut butter. Do not let it burn.

Add the onion, bell pepper, and celery. Cook for about 6 minutes, stirring frequently. Add the garlic and cook for 30 seconds.

Gradually whisk in the warm stock, scraping up any browned bits. Stir in the Worcestershire sauce, hot sauce, bay leaf, thyme, and remaining ½ teaspoon salt.

Return the alligator and its juices to the pot. Bring to a gentle simmer, then reduce the heat to low. Cover partially and cook for 45–60 minutes, stirring occasionally, until the meat is tender and reaches at least 160°F internally. Add a little stock or water if the gravy becomes too thick.

Remove the bay leaf. Taste and adjust the salt, Cajun seasoning, or hot sauce. Stir in the green onions and parsley. Serve over hot white rice.