In a slow cooker, combine the beef chuck, beef broth, water, soy sauce, hoisin sauce, sesame oil, ginger, garlic, and brown sugar. Stir well to combine.
Cover and cook on low for 6-8 hours or on high for 3-4 hours until the beef is tender.
About 30 minutes before serving, add the ramen noodles and bok choy to the slow cooker. Stir to combine and cover again.
Once the noodles are cooked, taste and adjust seasoning with salt and pepper as needed.
Serve the ramen in bowls, topped with sliced green onions and a soft-boiled egg if desired.