Place the chicken thighs in the slow cooker. In a small bowl, whisk together the honey, minced garlic, soy sauce, ketchup, rice vinegar, and sesame oil until smooth.
Pour the sauce over the chicken and turn the pieces to coat evenly. Cover and cook on low for 5 hours or on high for 3 hours until the chicken is tender.
Add the broccoli florets to the slow cooker during the final 45 minutes of cooking so they soften slightly but stay bright green.
Remove the chicken and shred or slice it, then return it to the slow cooker and stir to coat with the sauce.
Spoon the chicken and broccoli over the cooked rice and sprinkle with sesame seeds and green onions before serving.