In a medium bowl, season the chicken with salt, black pepper, and cornstarch. Drizzle with 1 teaspoon avocado oil and toss to coat.
In a small bowl, whisk together all the sauce ingredients until smooth. Set aside.
Heat 1 tablespoon of avocado oil in a large skillet over medium-high heat. Add onion and sauté for 1 minute.
Add the chicken and cook until it is no longer pink and fully cooked, about 4-5 minutes. Deglaze the pan with water if needed, then remove chicken and onion to a plate.
Add another tablespoon of avocado oil to the pan. Add broccoli and bell pepper and sauté for 2 minutes until crisp-tender.
Return chicken and onion to the pan. Pour in the sauce and stir to combine. Cook for 1 minute, or until the sauce thickens.
Serve hot over rice, garnished with parsley or green onions if desired.