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 about 3-4 minutes until browned, then remove from the skillet and set aside.
In the same skillet, add the remaining tablespoon of vegetable oil. Add the shrimp and cook for 2-3 minutes until they turn pink. Remove the shrimp and set aside with the steak.
Add the sliced bell peppers and snap peas to the skillet. Stir-fry for about 3-4 minutes until the vegetables are tender-crisp. Add the minced garlic and ginger, cooking for an additional 1 minute until fragrant.
In a small bowl, mix together the soy sauce, oyster sauce, cornstarch, water, and sesame oil. Pour this sauce over the vegetables in the skillet, stirring to combine.
Return the cooked steak and shrimp to the skillet, tossing everything together until heated through and well-coated with the sauce. Cook for another 2 minutes.
Serve the stir-fry over cooked rice or noodles.