Marinate the chicken by combining the sliced meat with 1 tablespoon soy sauce and 1 tablespoon cornstarch in a bowl. Let it sit for 10 minutes while you chop vegetables.
Whisk together the chicken broth, oyster sauce, remaining soy sauce, sesame oil, and cornstarch slurry in a small jar or bowl. Set aside.
Heat 1 tablespoon of oil in a large skillet or wok over medium-high heat. Once hot, add the chicken in a single layer. Cook for 3-4 minutes per side until golden and cooked through. Remove chicken to a plate.
Add the remaining tablespoon of oil to the same pan. Add carrots and broccoli. Stir-fry for 2 minutes. Add a splash of water and cover for 1 minute to steam slightly.
Toss in the bell peppers, snap peas, ginger, and garlic. Stir-fry for another 2 minutes until vegetables are crisp-tender.
Return the cooked chicken to the pan. Give the sauce mixture a quick whisk and pour it over the ingredients.
Toss everything together until the sauce bubbles and thickens, coating the food evenly. This should take about 30-60 seconds. Remove from heat immediately and serve.
