In a large skillet, heat the vegetable oil over medium-high heat. Sear the beef chuck roast on all sides until browned, about 4-5 minutes per side. Transfer the roast to a slow cooker.
In a bowl, whisk together the beef broth, soy sauce, brown sugar, gochujang, rice vinegar, minced garlic, minced ginger, sesame oil, and black pepper. Pour the mixture over the beef in the slow cooker.
Cover and cook on low for 8 hours or high for 4 hours, until the beef is tender and easily shredded with a fork.
Once cooked, remove the beef from the slow cooker and shred it using two forks. Return the shredded beef to the slow cooker and stir to coat it in the sauce.
Warm the tortillas in a skillet or microwave. Assemble the tacos by placing a generous portion of the beef mixture on each tortilla. Top with shredded cabbage, chopped green onions, and cilantro. Serve with lime wedges on the side.