Place the sliced chicken breast in a medium mixing bowl. Add soy sauce, oyster sauce, hoisin sauce, and cornstarch. Toss until the chicken is evenly coated, then let it sit for at least 15 minutes to absorb the flavors.
In a large wok or deep skillet, heat one tablespoon of vegetable oil over medium-high heat.
Once hot, add the marinated chicken and stir-fry for about 5 to 7 minutes, or until the meat is fully cooked and lightly browned. Remove the chicken from the pan and set it aside.
Add the remaining tablespoon of oil to the same skillet. Toss in the onion, red bell pepper, broccoli florets, snap peas, and carrot slices. Stir-fry for another 5 to 7 minutes, or until the vegetables are vibrant and tender-crisp.
Stir in the minced garlic and grated ginger. Cook for an additional 1 to 2 minutes, allowing the aromatics to release their fragrance.
Return the cooked chicken to the skillet with the vegetables. Pour in the chicken broth and mix thoroughly to combine all ingredients.
Continue cooking for 2 to 3 more minutes, allowing the liquid to slightly reduce and thicken, coating everything in a savory glaze.
Finish with a sprinkle of green onions and sesame seeds before serving hot.