Whisk together the soy sauce, chicken broth, oyster sauce, cornstarch, and sesame oil in a small bowl until smooth. Set aside.
Heat 1 tablespoon of oil in a wok or large skillet over medium-high heat. Add the chicken and cook for 4-5 minutes until browned and cooked through. Remove chicken from the pan and set aside.
Add the remaining tablespoon of oil to the same pan. Add carrots and broccoli. Stir fry for 2 minutes. Add bell pepper and snap peas, cooking for another 2-3 minutes until veggies are crisp-tender.
Stir in the garlic and ginger, cooking for 30 seconds until fragrant.
Return the chicken to the pan. Give the sauce a quick whisk and pour it over the mixture. Toss everything together for 1-2 minutes until the sauce thickens and coats the ingredients glossy.
Serve immediately over steamed white rice.