Prep your ingredients. This stir-fry comes together quickly, so have everything ready before you start cooking. Slice your beef, chop your vegetables, mince your garlic and ginger, and slice your green onions.
Make the sauce. In a small bowl, whisk together soy sauce, brown sugar, mirin, honey, rice vinegar, and sesame oil until the sugar is dissolved. In a separate small bowl, mix cornstarch and water until smooth, then whisk this slurry into the sauce. Set aside.
Heat your wok. Place your wok or large skillet over high heat and add 1 tablespoon of vegetable oil. Once it's shimmering hot (you'll see little ripples in the oil), it's ready.
Cook the beef in batches. Add half the beef in a single layer and let it sear undisturbed for about 1 minute. Then stir-fry for another 1-2 minutes until browned but not fully cooked through. Remove to a plate and repeat with the remaining beef.
Stir-fry the aromatics. Add the remaining tablespoon of oil to the wok. Add garlic, ginger, and the white parts of the green onions. Stir-fry for 30 seconds until fragrant but not browned.
Add the vegetables. Starting with the hardest vegetables first (like carrots and broccoli), stir-fry for 2-3 minutes. Then add quicker-cooking vegetables (like bell peppers and snap peas) and continue stir-frying for another 2 minutes until vegetables are crisp-tender.
Return the beef to the wok. Add the seared beef and any accumulated juices back to the wok with the vegetables.
Sauce it up. Give your prepared teriyaki sauce a quick stir (the cornstarch may have settled), then pour it into the wok. Toss everything together and cook for 1-2 minutes until the sauce thickens and coats everything nicely.
Add the finishing touches. Toss in the cashews or water chestnuts if using, and the green parts of the green onions. Give everything a final toss.
Serve it up. Plate over hot rice or noodles, and garnish with sesame seeds, additional green onions, and red pepper flakes if desired.