Preheat oven to 375 degrees F (190 degrees C).
Season pork cubes with salt, pepper, and thyme to taste and place in a cast iron skillet.
Cook pork cubes in the preheated oven until cooked through, about 30 minutes. Transfer pork from skillet to a bowl, reserving drippings.
Cook and stir bacon in a 9-quart Dutch oven or heavy pot over medium heat until browned, 5 to 7 minutes. Remove bacon with a slotted spoon and place on a paper towel-lined plate, reserving bacon grease.
Cook and stir okra in the bacon grease over medium heat until lightly browned, about 5 minutes. Transfer okra to a bowl, reserving bacon grease. Cook and stir smoked sausage in bacon grease until browned, about 5 minutes. Add onion, bell pepper, celery, and garlic to sausage; cook and stir until softened, 5 to 10 minutes.
Stir 48 fluid ounces chicken stock into sausage mixture and bring to a simmer. Stir roux into broth mixture until dissolved and slightly thickened, 2 to 3 minutes. Slowly stir 48 fluid ounces chicken stock into thickened stock; bring back to a simmer.
Mix pork, pork drippings, bacon, chili powder, paprika, 2 teaspoons black pepper, file powder, rosemary, 1 teaspoon thyme, bay leaves, and Creole seasoning into thickened chicken stock; simmer, stirring often and skimming off fat, until flavors blend, about 1 hour.
Stir black-eyed peas, mustard greens, okra, diced tomatoes with green chile peppers, mushrooms, and remaining chicken stock into pork-stock mixture; simmer for 1 hour more.
You can make your own roux, (browned oil and flour), but the pre-made roux is so easy and convenient, cooked perfectly every time, and tastes just the same as if you spent 45 minutes making your own.
Allow the gumbo to simmer for a while before adjusting the seasoning. A really good smoked sausage will release plenty of seasoning on its own.
An 8 to 9 pound Boston butt (pork shoulder roast) will yield about 6 pounds of cubed pork.
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