Cut the deer liver into roughly 2-ounce chunks. In a container large enough to hold the liver, combine 1 ½ cups of cold water with 1 teaspoon of kosher salt and stir until the salt dissolves. Add the liver, cover, and refrigerate for 8 to 12 hours.
Drain the liver and rinse it thoroughly under cold running water. Transfer it to a clean container and add milk to cover it completely. Cover and refrigerate for another 8 to 12 hours.
Drain the milk and rinse the deer liver again under cold running water. Pat dry, then chop the liver fine. Taking the time to chop it into small pieces allows the liver to mingle with the sausage and vegetables instead of leaving large pieces scattered through the finished rice.
Heat 1 tablespoon of the vegetable oil in a 6- or 8-quartDutch oven or heavy pot over medium-high heat. Add the finely chopped deer liver and ground pork. Cook, stirring frequently and breaking up the meat as it cooks, until browned, about 4 minutes. Season with 1 ½ teaspoons of the Tony's Creole seasoning, then transfer the cooked meat mixture to a large plate.
Add the remaining 1 tablespoon of vegetable oil to the now-empty Dutch oven. Add the onion, green bell pepper, celery, and garlic. Cook, stirring frequently, for about 2 minutes. Stir in the remaining 1 ½ teaspoons of Tony's and cook for another 2 minutes. The vegetables should begin to soften while picking up the flavor left behind by the browned meat.
Pour in the chicken broth and add the bay leaves. As the broth heats, scrape the bottom of the pan thoroughly to loosen the browned bits. Bring to a boil, then transfer the liver/pork mixture back to the Dutch oven, sprinkle in the sugar, and stir to combine.
Reduce the heat and simmer for 5 minutes. This brief simmer gives the broth time to mingle with the deer liver, sausage, vegetables, and seasonings before adding the rice.
Add the chilled cooked rice and stir thoroughly, making sure the deer liver, sausage, and vegetables are evenly distributed throughout the rice. Continue cooking for about 3 minutes, stirring as needed, until the rice is heated through.
Remove the pan from the heat and discard the bay leaves. Taste and add more Tony's if needed. Serve immediately with green onions and your favorite hot sauce on the side.