Cover pork shanks with water in a large pot over medium heat; bring to a boil.
Reduce heat to low, cover the pot, and gently simmer pork shanks until tender, about 2 hours. Skim foam that forms on the surface of water as pork cooks; pour in more water as needed. Drain pork shanks and allow to cool, about 15 minutes. Remove surface moisture with paper towels.
Pour root beer into a saucepan over medium heat and bring to a boil. Reduce heat to medium-low and simmer until reduced to 4 cups, about 20 minutes.
Stir apple butter and hot sauce into root beer; reduce heat to low and simmer to keep warm, stirring occasionally, while frying shanks.
Heat vegetable oil in a deep-fryer or large saucepan to 350 degrees F (175 degrees C).
Gently lower pork shanks into hot oil, 2 or 3 at a time, and deep-fry until meat is crisp and brown, about 3 minutes per batch. Drain on a plate lined with paper towels.
Serve pork shanks slathered with hot apple butter sauce.