Preheat your smoker to 250°F for indirect cooking. Season the cubed chuck roast generously with salt, black pepper, garlic powder, and Korean BBQ rub, then place directly on the smoker grates and cook for about 2 hours until a deep, flavorful bark forms.
In a bowl, whisk together brown sugar, minced garlic, ginger paste, gochujang, soy sauce, rice wine vinegar, sesame oil, beef broth, and cornstarch until smooth. Transfer the smoked beef cubes to a Dutch oven and pour the braising liquid over the top.
Cover the Dutch oven and return it to the smoker or place in a 300°F oven. Braise for about 2 hours, or until the beef is fork-tender and easily shreds apart.
Remove the beef from the liquid and shred using two forks, then return it to the pot and toss in the thickened sauce until fully coated. The beef should be juicy, sticky, and deeply flavorful.
In a separate bowl, combine coleslaw mix, mayonnaise, apple cider vinegar, green onions, everything bagel seasoning, and sugar. Mix thoroughly and refrigerate until ready to assemble.
Toast the slider buns lightly over the grill or in a skillet until golden. Spread spicy mayo made from mayonnaise and sriracha on the buns, pile on shredded beef, top with Asian slaw, and serve immediately while warm.