Whisk the sauce: In a small bowl, mix honey, soy sauce, olive oil, garlic, vinegar, thyme, salt, and pepper.
Layer the crock pot: Place chicken in the bottom of your slow cooker. Arrange carrots, potatoes, and onion around it.
Add the sauce: Pour the honey garlic mixture evenly over the top.
Cook: Cover and cook on Low for 6–7 hours or High for 3–4 hours until chicken is tender and vegetables are cooked.
Add broccoli: Stir in broccoli 30 minutes before serving so it stays crisp and green.
Serve: Garnish with parsley and sesame seeds, and drizzle with extra sauce from the pot.