Heat 1/4 cup of the olive oil in large heavy nonstick pot or Dutch oven over medium-high heat. Stir in the onions, bell peppers, celery, salt, crushed red pepper flakes, cayenne, and bay leaves. Cook, stirring occasionally, until the vegetables are soft and lightly golden, about 5 minutes. Add 3 tablespoons of the flour and cook, stirring, to cook the flour without browning, 1 to 2 minutes. Add the tomatoes, chicken stock, Worcestershire, and pepper sauce. Bring to a boil, then reduce the heat to medium-low.

Place several pieces of alligator meat at a time on a work surface covered with plastic wrap. Cover the meat with plastic wrap and pound with a meat mallet until 1/4 inch thick. Cut into 2-inch strips.

Combine the remaining 1/2 cup flour and the Essence in a medium bowl. Dredge the alligator pieces in the seasoned flour, shaking off any excess.

Heat 2 tablespoons of the olive oil in a large nonstick skillet over medium-high heat. Add half of the meat and fry until golden brown, turning once, 3 to 4 minutes per side. Transfer to a platter. Heat the remaining 2 tablespoons oil in the skillet and repeat with the remaining alligator.

Add the meat to the sauce. Increase the heat under the sauce to medium-high and bring to a gentle rolling boil. Reduce the heat to medium-low. Simmer uncovered, stirring occasionally, until the meat is tender, about 2 hours. Remove and discard the bay leaves.

To serve, spoon the rice into soup bowls, top with the meat and sauce, and garnish with the green onions and parsley.