Preheat your oven to 425°F (220°C) and line a large rimmed baking sheet with foil.
Pat the 2 pounds chicken thighs dry and toss them in a bowl with ⅓ cup of the teriyaki sauce. Reserve the remaining ⅔ cup, because the sugary sauce will scorch if it roasts the whole time, so we glaze with it at the end instead.
Toss the broccoli, bell peppers, sliced carrots, and red onion with the 2 tablespoons vegetable oil, and ¼ teaspoon black pepper
Arrange the chicken down the center of the sheet pan. Scatter the veggies along both sides of the chicken in a single layer.
Roast for 20 minutes, until the chicken reaches 175°F (80°C) and the vegetables are tender with browned edges. Thighs want that higher pull temperature, not 165°F, since that is where they turn silky.
Brush the chicken generously with the reserved teriyaki sauce and drizzle some over the veggies as well, then switch the oven to broil for 2 to 3 minutes, until the glaze is bubbling and caramelized. Watch it closely, the sugar goes from glossy to burnt fast.
Spoon any pan juices over the top, then serve over the 3 cups warm rice, finished with the 2 tablespoons sesame seeds and sliced green onions.