Place the beef chuck roast pieces into the basin of a slow cooker.

In a medium bowl, whisk together the soy sauce, brown sugar, 1/4 cup water, mirin, sesame oil, minced garlic, grated ginger, and gochugaru (if using). Mix well until the brown sugar is mostly dissolved.

Pour the sauce mixture evenly over the beef in the slow cooker, ensuring the meat is well coated.

Cover and cook on low for 6 to 8 hours, or on high for 3 to 4 hours, until the beef is fork-tender.

Remove the beef from the slow cooker and place it on a cutting board. Use two forks to shred the meat completely. Set aside.

Skim any excess fat from the liquid remaining in the slow cooker. If you desire a thicker sauce, mix the 1 tbsp cornstarch with 2 tbsp cold water to create a slurry. Stir the slurry into the sauce in the slow cooker and cook on high for 10-15 minutes until thickened. (Alternatively, just simmer the sauce on the stovetop if the slow cooker doesn't allow switching to high).

Return the shredded beef to the sauce and toss gently to coat thoroughly. Let it simmer in the sauce for a final 10 minutes to absorb the flavor.

Serve the Korean beef hot over steamed white rice or alongside lettuce wraps. Garnish generously with toasted sesame seeds and sliced green onions.