In a medium pan over medium heat, whisk together the teriyaki sauce, honey, sesame oil, garlic, ginger, cornflour until combined. Bring to a simmer, stirring frequently, until sauce thickens and bubbles. Remove from heat and set aside.
Preheat oven to 200 degrees, Gas Mark 6. Line a large tray with foil. Season each side of the chicken and potatoes with salt and black pepper then drizzle over half the sauce.
Cook in preheated oven for 30 minutes. Arrange the broccolini and carrots around the chicken.
Season and drizzle with some sauce. Return to the oven and bake for another 20 minutes or until the chicken is cooked through and juices run clear.
Remove tray from oven, and drizzle with remaining sauce. Serve with rice or quinoa.
If chicken is not done, remove vegetables from tray to prevent overcooking then return the chicken back to the oven until cooked through.
Potatoes may seem like an unusual addition here but my kids really like them. Omit if you wish and substitute with other vegetables.