Place the cubed beef chuck roast into the bottom of a 6-quart slow cooker.
In a medium bowl, whisk together the beef broth, soy sauce, brown sugar, rice vinegar, sesame oil, garlic, ginger, and red pepper flakes.
Pour the sauce mixture over the beef and stir to ensure even coating.
Cover and cook on low for 7 to 8 hours or on high for 3 to 4 hours until the beef is fork-tender.
Add the frozen vegetables to the slow cooker 30 minutes before the end of the cooking time.
Discard the seasoning packets from the ramen noodles and place the dry noodles into the slow cooker, submerging them in the liquid.
Cook for an additional 10 to 15 minutes until the noodles are soft.
Stir the mixture to break up the noodles and shred the beef slightly, then serve garnished with sliced green onions.