In a large skillet or wok, heat the vegetable oil over medium-high heat.
Add the minced garlic and ginger, and sauté for about 1 minute until fragrant.
Add the sliced chicken to the skillet and cook until it is no longer pink in the center, about 5-7 minutes.
Once the chicken is cooked, add the mushrooms, snow peas, carrot, and bamboo shoots to the skillet. Stir-fry for an additional 3-4 minutes until the vegetables are tender-crisp.
In a small bowl, whisk together the soy sauce and oyster sauce. Pour the sauce mixture over the chicken and vegetables in the skillet.
Stir in the dissolved cornstarch mixture, which will help thicken the sauce. Cook for another minute or until the sauce has thickened.
Season with salt and pepper to taste.
Serve the Moo goo gai pan hot over steamed rice.