Velvet the Steak: In a medium bowl, mix the beef with water, oil, cornstarch, and salt. Stir thoroughly to coat the meat and set aside.
Prepare the Pepper Seasoning: In a small bowl, combine black pepper, white pepper, Sichuan peppercorns, and salt.
Season the Beef: Sprinkle two-thirds of the pepper mixture over the beef. Use your hands or a spoon to press and coat the seasoning onto the meat. Reserve the remaining pepper blend for later.
Mix the Sauce: In another small bowl, combine the warm beef stock with oyster sauce, soy sauce, ketchup, sugar, and sesame oil. Stir until the sugar fully dissolves.
Sear the Beef: Heat a wok over high heat until it begins to smoke. Add 1 tablespoon of oil and swirl to coat the sides. Add the beef in a single layer (fat side down for visible fat pieces). Sear for about 30 seconds on the first side without moving, then flip and cook the other side for 20 seconds. Stir-fry briefly to brown all sides for about 30 to 60 seconds total. Transfer the meat to a plate.
Cook the Aromatics and Vegetables: Return the wok to medium-high heat and add the remaining tablespoon of oil. Sauté the ginger for about 5 to 10 seconds. Add the garlic, green bell pepper, and red bell pepper. Stir-fry for about 1 minute until the edges are slightly browned and tender.
Add Remaining Veggies and Seasoning: Toss in the red onion, mushrooms, and remaining pepper seasoning. Pour the Shaoxing wine around the sides of the wok to help loosen any caramelized bits. Stir-fry everything together for 1 minute.
Combine and Finish the Dish: Bring the sauce mixture to a simmer. In a small bowl, stir together cornstarch and water to form a slurry. Slowly drizzle half the slurry into the simmering sauce while stirring until it thickens slightly. Add the seared beef along with any juices. Mix everything together until evenly coated. If needed, add more slurry and stir-fry for another 10 to 15 seconds until the sauce thickens to your liking. Serve immediately.