In a medium bowl, combine the thinly sliced beef with 2 tbsp soy sauce, 1 tbsp rice vinegar, 1 tbsp cornstarch, 1 tsp sesame oil, and black pepper. Toss until the beef is evenly coated. Let it marinate for at least 10-15 minutes while you prepare the other ingredients.
In a small bowl or measuring cup, whisk together all the stir-fry sauce ingredients: 1/3 cup soy sauce, oyster sauce, rice vinegar, brown sugar, minced garlic, grated ginger, 1 tsp cornstarch, and water. Set aside.
Heat a large wok or skillet over high heat until very hot. Add 1 tablespoon of vegetable oil. Add the marinated beef in a single layer, working in batches if necessary to avoid overcrowding. Sear without moving for 1 minute, then stir-fry for another 1-2 minutes until just browned but not fully cooked through. Transfer the beef to a clean plate.
Add the remaining 2 tablespoons of oil to the hot wok. Add the broccoli florets and stir-fry for 2 minutes. Add the sliced onions and bell peppers and stir-fry for another 2-3 minutes until they begin to soften. Finally, add the snow peas and stir-fry for 1 more minute. The vegetables should be crisp-tender and brightly colored.
Return the cooked beef and any accumulated juices to the wok with the vegetables. Give the prepared sauce a quick re-whisk and pour it over everything. Toss to combine. Bring the sauce to a simmer and cook, stirring constantly, for 1-2 minutes until the sauce has thickened and glossy and everything is heated through.
Remove from heat. Garnish with sliced green onions and toasted sesame seeds. Serve immediately over steamed rice or noodles in bowls.