In a mixing bowl combine soy sauce and cornstarch; whisk until completely incorporated.
Whisk in brown sugar, sesame oil, and chicken broth; set aside.
Prepare chicken by cutting it into small cubes or long thin strips; set aside.
Add vegetable oil to a Wok or use a large nonstick skillet; set wok over high heat.
Once oil is hot, add garlic and ginger; stir and cook for 10 seconds.
Add onion and continue to cook for 1 more minute, stirring frequently, just until onion softens.
Stir in the chicken and cook for 2 to 3 minutes, or until chicken is white; stir frequently.
Add in prepared carrots, peppers, and mushrooms; continue to cook for 2 minutes.
Stir the sauce that you prepared earlier, and then add it to the wok; cook for an additional 3 to 4 minutes, stirring very frequently, until sauce has thickened, veggies are crisp-tender, and chicken is cooked through.
Remove from heat.
Garnish with green onions, sesame seeds, and pepper flakes.
Serve over rice.