In a small bowl, mix the soy sauce, oyster sauce, cornstarch, water, and sesame oil. Set aside.
Heat 1 tablespoon of vegetable oil in a large skillet or wok over medium-high heat. Add the sliced steak and season with salt and pepper. Cook for 2-3 minutes until browned. Remove the steak from the skillet and set aside.
In the same skillet, add the remaining tablespoon of vegetable oil. Add the garlic and ginger, stirring for about 30 seconds until fragrant.
Add the bell pepper, snap peas, and broccoli to the skillet. Stir-fry for 3-4 minutes until the vegetables are tender-crisp.
Return the steak to the skillet and add the shrimp. Cook for an additional 3-4 minutes until the shrimp are pink and opaque.
Pour the sauce mixture over the stir-fry and toss everything together until well coated. Cook for another minute until the sauce thickens slightly.
Serve hot over cooked rice or noodles.