First, in a deep stockpot, bring to a boil enough water to completely cover the mirlitons. Add crab boil to water. Then reduce the heat to medium range and at a gentle bubble poach the mirlitons until you can pierce them easily through- and-through with an ice pick. At that point, take them out of the water and allow them to cool to room temperature. Then slice them in half, remove the center seed, peel away the outer skin, and cut them into medium-size cubes.
In the meantime, take a 5 or 6 quart heavy aluminum or stainless steel Dutch oven, heat the bacon drippings to high, toss in the chopped onions and the celery, and sauté the mixture until it wilts (but don’t let it brown). Then, pour in the chicken stock and bring it to a slow boil, add the chopped mirlitons, cover the pot, and simmer it until piping hot (this should take about 20 minutes or so over medium-low heat).
Next, add the milk, the cream, and the butter to the soup base and stir the mixture continuously until it, too, begins to bubble. Then reduce the fire once again and stir in the thyme, the vegetable seasoning, the hot sauce, the crumbled bacon, the chopped shrimp, the gravy flour and the pepper cheese. When all the ingredients are thoroughly blended, put the lid back on the pot, reduce the fire to low, and simmer the soup for another 20 minutes to allow all the flavors to marry.