1. To make marinade, place honey, gluten free soy sauce, olive oil and gluten free Vegemite in a large bowl and mix well. Add the chicken drumsticks and toss to coast. Place in the fridge for at least 2 hours.
2. Preheat oven to 180 degrees. Place marinated chicken onto a baking tray and pour over remaining marinade. Cook, turning halfway, for 20-30 minutes or until chicken is sticky and cooked through. Once cooked, sprinkle chicken with sesame seeds.
3. While the chicken is cooking, cook the broccolini in a saucepan of boiling water for 2-3 minutes or until tender.
4. Cook rice in a separate saucepan according to packet instructions.
5. Divide broccolini and rice between serving plates, top with drumsticks and serve with lime wedges.