In a small bowl, whisk together soy sauce, vegetarian oyster sauce, sesame oil, and cornstarch until well combined.
Heat vegetable oil in a large skillet or wok over medium-high heat. Sear the chicken breasts until golden brown on both sides (about 5-6 minutes). Remove from skillet and set aside.
In the same skillet, add onions and garlic; sauté until fragrant (about 1-2 minutes).
Add sliced mushrooms and bell peppers; stir-fry for an additional 3-4 minutes until vegetables are tender-crisp.
Return chicken to the skillet; pour in the prepared sauce and toss everything together. Simmer for about 2-3 minutes until the sauce thickens slightly.
Garnish with green onions or sesame seeds if desired before serving.