Preheat oven to 425°F. Use 2 sheet pans and lightly grease, spray with non-stick cooking spray, or line with parchment paper.
In a medium bowl, mix together sauce ingredients until combined. Set aside.
In a small bowl, mix spice rub ingredients until well combined. Rub over chicken, coating both sides. Place chicken on one baking sheet in single layer.
Spread vegetables out on second baking sheet. Drizzle 1 tablespoon oil evenly over vegetables, sprinkle with salt and pepper.
Place oven racks at middle top and middle bottom of oven. Place one sheet pan on each oven rack with vegetables on top. Bake 20 minutes, stir the vegetables and continue cooking 15 more minutes until chicken reaches 165°F on meat thermometer inserted at thickest part of thigh.
Remove pans from oven and transfer chicken pieces to pan with the vegetables. Brush chicken with sesame sauce. Lightly dab sauce onto vegetables (optional). Place pan back in oven for 3 minutes to caramelize sauce. Repeat for a second layer of sauce.
Remove pan from oven, sprinkle chicken with sesame seeds. Serve with vegetables and remaining sauce on the side.