Step 1: Prepare the beef. In a medium bowl, combine the thinly sliced flank steak with 1 tablespoon soy sauce, 1 tablespoon cornstarch, and 1 teaspoon sesame oil. Toss to coat evenly. Let marinate at room temperature for at least 15 minutes while you prep the vegetables.
Step 2: Prepare the vegetables. Chop garlic and mince ginger. Cut broccoli into small florets, slice bell pepper into thin strips, and julienne carrots. Have all your prepped ingredients ready by your cooking station (mise en place).
Step 3: Make the stir-fry sauce. In a small bowl, whisk together the beef broth, 2 tablespoons soy sauce, rice vinegar, honey (or brown sugar), 2 teaspoons cornstarch, 1 teaspoon sesame oil, and black pepper. Set aside.
Step 4: Cook the beef. Heat 1 tablespoon of vegetable oil in a large wok or heavy-bottomed skillet over high heat until shimmering. Add half of the marinated beef in a single layer. Cook for 1-2 minutes per side until nicely browned. Remove the cooked beef from the wok and set aside. Repeat with the remaining beef, adding a little more oil if needed. Do not overcrowd the pan.
Step 5: Sauté aromatics. Add the remaining 1 tablespoon of vegetable oil to the wok. Add the minced garlic and ginger and stir-fry for about 30 seconds until fragrant, being careful not to burn them.
Step 6: Cook the harder vegetables. Add the broccoli florets and julienned carrots to the wok. Stir-fry for 3-4 minutes, tossing constantly, until they are bright green and slightly tender-crisp.
Step 7: Add the softer vegetables. Add the sliced bell pepper and snap peas (if using) to the wok. Stir-fry for another 2-3 minutes until they are vibrant and crisp-tender.
Step 8: Thicken the sauce. Give the prepared stir-fry sauce a quick whisk again, then pour it into the wok with the vegetables. Bring it to a simmer, stirring constantly, until the sauce thickens and becomes glossy, about 1-2 minutes.
Step 9: Combine and serve. Return the cooked beef to the wok and toss everything together to coat the beef and vegetables evenly with the thickened sauce. Cook for just another minute to heat through. Serve immediately over steamed rice or noodles.