Brown the ground beef and diced onion in a skillet over medium heat until the beef is no longer pink. Drain any excess fat.
Add the browned beef mixture to the slow cooker along with the minced garlic, soy sauce, beef broth, brown sugar, sesame oil, and ground ginger. Stir to combine.
Cover and cook on low for 4 hours.
About 30 minutes before serving, steam the broccoli florets until bright green and tender-crisp.
Serve the beef mixture over the cooked white rice. Top each bowl with steamed broccoli, sliced green onions, and sesame seeds.