Whisk all sauce ingredients except the cornstarch slurry in a small bowl; set aside. Toss the sliced protein with 1 tbsp cornstarch, salt, and pepper.
Heat 1 tbsp oil in a large skillet or wok over HIGH heat until shimmering. Add half the protein in a single layer; sear undisturbed 1-2 minutes, then stir-fry 2-3 minutes until cooked through. Transfer to a plate. Repeat with remaining protein.
Add the remaining 1 tbsp oil. Stir-fry the hard vegetables (broccoli, carrots) 2-3 minutes, then add quick-cooking vegetables (bell peppers, snow peas) plus garlic and ginger; stir-fry 1-2 minutes until fragrant and crisp-tender.
Return the protein to the pan. Pour in the sauce and bring to a boil, then drizzle in the cornstarch slurry, stirring, until the sauce turns glossy and thick enough to coat everything, about 1 minute.
Remove from heat, sprinkle with green onions and sesame seeds, and serve immediately over rice or noodles.