In a bowl, combine the shrimp, soy sauce, and cornstarch. Mix well and let sit for about 10 minutes while you prepare the vegetables.
Slice the bell pepper, and trim the snap peas. Mince the garlic and ginger.
In a large skillet or wok, heat 1 tablespoon of vegetable oil over medium-high heat.
Once the oil is hot, add the marinated shrimp. Cook for 2-3 minutes until the shrimp turns pink and opaque. Remove from the skillet and set aside.
In the same skillet, add the remaining tablespoon of vegetable oil. Add the minced garlic and ginger, stirring for about 30 seconds until fragrant. Add the bell pepper, broccoli, and snap peas, and stir-fry for about 3-4 minutes until the vegetables are tender-crisp.
Return the cooked shrimp to the skillet. Add the oyster sauce and sesame oil. Toss everything together and cook for an additional 1-2 minutes until heated through. Season with salt and pepper to taste.
Serve the shrimp stir fry over cooked rice or noodles.