Place 1 teaspoon of vegetable oil in a large pan and heat over medium high heat.
Add the broccoli, mushrooms, and yellow bell pepper to the pan. Cook for 5-6 minutes or until vegetables are tender.
Remove the vegetables from the pan; transfer to a plate and cover with foil to keep warm.
Wipe the pan clean with a paper towel, then heat the remaining tablespoon of vegetable oil over high heat.
Add the chicken to the pan in a single layer and season with salt and pepper to taste.
Cook for 3-4 minutes per side, or until chicken is browned and cooked through.
Lower heat to medium, add the garlic and cook for 30 seconds.
Add the vegetables back to the pan.
In a small bowl, whisk together the chicken broth, brown sugar, soy sauce, sesame oil, and cornstarch.
Pour the sauce over the chicken mixture and bring to a simmer.
Simmer for 1-2 minutes or until sauce has just thickened.
Serve immediately, with steamed rice if desired.
