In a saucepan, over high heat, bring the milk and 2 tablespoons of the butter to a boil. Season with salt. Stir in the grits, reduce the heat to medium low. Cook, stirring occasionally until the grits are tender, about 1 1/2 hours. In a saucepan, heat the olive oil. Season the alligator meat and flour with Creole seasoning. Toss the meat in the seasoned flour, coating completely. When the oil is hot, brown the alligator meat on all sides. Remove and set aside. Add the onions, green onions, celery, bell peppers, jalapenos, and garlic. Saute for 2 minutes. Add the herbs and bay leaves and continue sauteing for 1 minute. Stir in the tomatoes and stock. Season with cayenne, salt and pepper. Add the alligator. Simmer the sauce for about 30 minutes or until the alligator meat is tender. Stir in the remaining 2 tablespoons of butter. Stir the heavy cream into the grits. Season with salt and white pepper. To serve, spoon the grits in the center of each serving bowl. Spoon the alligator mixture over the grits. Garnish with green onions