Prepare a dark roux by combining extra virgin olive oil and flour in a heavy-bottomed pot over medium heat.

Stir constantly until the roux reaches a dark brown color.

Add minced onion, green onion, bell pepper, and celery to the roux.

Cover and cook until the onions are translucent, stirring occasionally.

Incorporate minced fresh tomatoes and continue cooking for 10 minutes, stirring frequently.

Pour in cool water and stir to create a thick liquid consistency.

Season with finely-minced garlic, Worcestershire sauce, lemon juice, salt, and Tabasco sauce to taste. Mix well.

Add the dry white wine and tomato sauce, ensuring thorough mixing.

Introduce the trimmed and cubed alligator meat to the sauce.

Add sufficient water to cover the alligator meat and other ingredients by approximately 2 inches. Stir to combine.

Bring the mixture to a boil, stirring frequently to prevent sticking.

Reduce the heat to low, cover the pot, and simmer for 3 to 4 hours, checking periodically and stirring to prevent the sauce from sticking, until the alligator meat is tender.

Serve the Alligator Sauce Piquant over cooked rice or spaghetti.

Garnish with Parmesan cheese, if desired.

Freeze any leftover sauce in serving-size containers for future enjoyment.