Whisk soy sauce, broth, oyster sauce, rice vinegar, brown sugar, cornstarch, sesame oil, garlic, ginger, and red pepper flakes until smooth.
Toss sliced pork with 2 teaspoons of the sauce to lightly coat. Set aside while you heat the pan.
Heat 1 tablespoon oil in a large skillet or wok over high heat until shimmering.
Stir-fry half the pork for 2–3 minutes until just browned. Transfer to a plate and repeat with remaining pork.
Add remaining 1 tablespoon oil. Stir-fry broccoli and carrots for 2 minutes.
Add bell pepper and snap peas. Cook, tossing, 2 minutes more until crisp-tender.
Return pork and any juices. Pour in the sauce, then stir until bubbling and glossy, 1–2 minutes.
Remove from heat and fold in green onions. Serve immediately.