In a bowl, toss the chicken pieces with 1 tablespoon of cornstarch and 1 tablespoon of soy sauce. Make sure the chicken is evenly coated. This helps create a nice crust when it cooks.

In a separate bowl, whisk together the remaining 2 tablespoons of cornstarch, the remaining soy sauce, oyster sauce, brown sugar, black pepper, and chicken broth. Set this aside.

Heat 1 tablespoon of vegetable oil in a large skillet or wok over medium-high heat. Add the chicken and cook until it's browned and cooked through, about 5-7 minutes. Remove the chicken from the skillet and set it aside.

Add the remaining 1 tablespoon of oil to the skillet. Add the chopped onion and bell peppers and cook until they're tender-crisp, about 3-5 minutes.

Add the minced garlic and ginger to the skillet and cook for about 30 seconds, until fragrant.

Return the cooked chicken to the skillet with the vegetables. Pour the sauce over the chicken and vegetables.

Bring the sauce to a simmer, stirring constantly, until it thickens and coats the chicken and vegetables nicely. This should only take a minute or two.

Serve immediately over rice or noodles. Garnish with sesame seeds or chopped green onions, if desired.