Place the thinly sliced flank steak in a large bowl and toss with the cornstarch until the slices are evenly coated.
Heat 1 cup vegetable oil in a large skillet or wok over medium-high heat until hot but not smoking.
Working in batches if needed, fry the coated beef slices 1–2 minutes until browned and cooked through, stirring to cook evenly; transfer to a paper towel-lined plate and discard the frying oil.
In a medium saucepan over low–medium heat, add 2 teaspoons sesame oil (or vegetable oil), then add the minced garlic and minced ginger and cook, stirring, for about 30 seconds.
Add the dark brown sugar, soy sauce, and water to the saucepan and whisk to combine; simmer until slightly thickened, about 5–10 minutes.
Add the cooked beef back to the skillet, pour in the sauce, and cook over medium heat 2–3 minutes until the sauce thickens and coats the beef.
Stir in the green onions, sprinkle with sesame seeds, and serve immediately over rice if desired.