Place the sliced flank steak and 1/3 cup cornstarch in a large zip-top bag. Seal and shake vigorously until the beef is evenly coated; set aside about 15 minutes.
Heat a large 14-inch skillet over medium-high heat and add 1 tablespoon of the vegetable oil. Add half the beef in a single layer and cook undisturbed 3–4 minutes, then flip and cook another 3–4 minutes until browned. Transfer to a plate and repeat with the remaining beef and the other tablespoon oil.
Reduce heat to medium and add the sesame oil to the skillet. Add the minced garlic and minced ginger and cook, stirring, about 1 minute until fragrant.
In a medium bowl, whisk together 1/2 cup low-sodium soy sauce, 1/3 cup brown sugar, 1/3 cup water, and 1 tablespoon rice vinegar. Pour the sauce into the skillet and cook 2–3 minutes, stirring, until the sugar dissolves.
In a small bowl, whisk 1 tablespoon cornstarch with 2 tablespoons water to make a slurry. Stir the slurry into the sauce and simmer over medium-low 1–2 minutes until the sauce thickens.
Return the cooked beef to the skillet and toss to coat in the sauce. Cook 1–2 minutes more until heated through, then serve immediately over rice. Garnish with green onions and sesame seeds if desired.
