Place the sliced beef, onion, garlic, ginger, soy sauce, fish sauce, beef broth, sesame oil, and red pepper flakes in the slow cooker. Stir to combine everything evenly.
Cover and cook on low for 5 hours.
Add the broccoli florets and sliced red bell peppers to the slow cooker. Stir gently, then cover and cook for 1 more hour on low until the vegetables are tender but still bright.
Turn off the heat and stir in the Thai basil leaves until they wilt slightly.
Serve the beef and vegetables with lime wedges on the side.