Place the thinly sliced flank steak in a large bowl and toss with the cornstarch until each piece is evenly coated; set aside.
Heat 1 cup vegetable oil in a large saucepan or deep skillet over medium-high heat until hot but not smoking.
Working in batches if needed, add the coated beef to the hot oil and fry, stirring, until browned and cooked through, about 1–2 minutes; transfer to a paper towel-lined plate and discard the frying oil (or carefully pour off and reserve if desired).
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 until fragrant.
Whisk in the dark brown sugar, soy sauce, and water into the saucepan and cook, stirring occasionally, until the sauce is slightly thickened, about 5–10 minutes.
Add the fried beef back into the pan with the sauce and cook over medium heat, stirring, until the sauce coats the beef and thickens further, about 2–3 minutes.
Stir in the sliced green onions, then transfer to a serving dish and sprinkle with sesame seeds; serve immediately over rice if desired.
