Slice the flank steak thinly against the grain and pat dry with paper towels.
Toss the beef with the cornstarch until evenly coated. Let it rest for 10 minutes.
In a small bowl, whisk together the soy sauce, brown sugar, water, garlic, ginger, hoisin sauce, and sesame oil.
Heat 1 tablespoon of vegetable oil in a large skillet or wok over medium-high heat.
Cook half of the beef for 2–3 minutes, turning occasionally until browned. Transfer to a plate and repeat with the remaining oil and beef.
If using vegetables, stir-fry them in the same skillet for 3–4 minutes until crisp-tender. Remove if necessary.
Pour the prepared sauce into the skillet and bring to a gentle simmer.
Cook for 2–3 minutes, stirring occasionally, until the sauce begins to thicken.
Return the cooked beef (and vegetables, if using) to the skillet and toss until evenly coated in the sauce.
Cook for another 2 minutes, allowing the sauce to glaze the beef.
Garnish with sliced green onions and sesame seeds.
Serve immediately over steamed jasmine rice or noodles.