Heat the vegetable oil in a large skillet or wok over medium-high heat. Add the sliced chicken and cook until browned and cooked through, about 5-7 minutes. Remove the chicken from the skillet and set aside.
In the same skillet, add the mushrooms, broccoli, bell peppers, snow peas, garlic, and ginger. Stir-fry the vegetables for about 3-4 minutes until they are tender-crisp.
In a small bowl, whisk together the soy sauce, oyster sauce, cornstarch, chicken broth, and sesame oil.
Return the cooked chicken to the skillet with the vegetables. Pour the sauce over the chicken and vegetables, stirring to combine. Cook for an additional 2-3 minutes until the sauce thickens and everything is heated through.
Season with salt and pepper to taste. Serve hot over cooked rice.