Prepare the Marinade: In a bowl, whisk together soy sauce, brown sugar, sesame oil, beef broth, water, grated ginger, minced garlic, and gochugaru. This will be the marinade for the roast.
Marinate the Beef: Place the beef chuck roast in a large resealable bag or dish and pour the marinade over it. Seal tightly and let it marinate in the refrigerator for at least 4 hours, or overnight for a deeper flavor.
Sear the Roast: In a large oven-safe pot or Dutch oven, heat a tablespoon of oil over medium-high heat. Remove the roast from the marinade and gently pat it dry. Season it with salt and pepper, then sear it on all sides until browned, about 4-5 minutes per side.
Add Vegetables: Remove the roast from the pot and set aside. In the same pot, add the quartered onions and carrot chunks, sautéing until just softened (about 3-4 minutes).
Combine and Cook: Return the roast to the pot, pour the reserved marinade over it, and add the green onions. Bring the pot to a boil, then cover with a lid or foil and transfer to a preheated 300°F (150°C) oven. Cook for about 3-4 hours, or until the meat is fork-tender.
Finish and Garnish: Once the roast is done, remove it from the oven. Let it rest for about 10-15 minutes before slicing. Serve the roast with the vegetables and drizzled sauce, garnished with sesame seeds and chopped green onions.