Combine gochujang, onion, vinegar, chicken stock, honey, brown sugar, ginger, soy sauce, mustard, garlic, cinnamon, salt, thyme, and black pepper together in a large bowl and mix well.
Dredge pork in the gochujang sauce on all sides. Pour sauce into a slow cooker and add the pork. Spoon some of the sauce on top of the pork. Cover and cook on Low until pork roast shreds easily with a fork, about 8 hours.
Preheat oven to 350 degrees F (175 degrees C).
Place roast in a large bowl and shred the meat with 2 forks. Pour the sauce from the slow cooker into a pot over medium-high heat. Cover and bring to a boil. Uncover; reduce heat to a simmer.
Mix 1 tablespoon butter and flour in a small bowl; combine with the sauce in the pot and mix well. Cook until heated through and slightly thickened, about 5 minutes. Remove from heat and stir again.
Spread remaining 3 tablespoons butter over insides of buns. Place on a baking sheet.
Toast in the preheated oven until golden brown, 5 to 7 minutes.
Pour the sauce into the bowl with the shredded pork and mix. Top pork with green onions. Spoon pork over the toasted buns.
