In a large skillet, heat the sesame oil over medium heat. Add the broccoli, red bell pepper, and shredded carrots. Sauté for about 5-7 minutes until the vegetables are tender-crisp. Season with salt and pepper to taste.
In a separate bowl, combine the shredded rotisserie chicken with the sweet chili sauce, mixing well to coat the chicken evenly.
Once the vegetables are cooked, add the sweet chili chicken mixture to the skillet and stir to combine. Cook for an additional 3-5 minutes until heated through.
To serve, divide the cooked brown rice among bowls. Top each bowl with the sweet chili chicken and vegetable mixture.
Garnish with sliced green onions and sesame seeds if desired.