In a medium bowl, whisk together the soy sauce, mirin, sake (or water), brown sugar, honey, grated ginger, and minced garlic. Set aside. In a separate small bowl, whisk together the cornstarch and cold water until smooth to create a slurry. Set aside.

Pat the thinly sliced flank steak dry with paper towels. This helps ensure a good sear. Heat the vegetable oil in a large skillet over medium-high heat until shimmering.

Add half of the beef to the hot skillet in a single layer. Do not overcrowd the pan, as this will steam the beef instead of searing it. Cook for 1-2 minutes per side until nicely browned. Remove the cooked beef to a plate and repeat with the remaining beef. Set all cooked beef aside.

Reduce the heat to medium. Pour the whisked teriyaki sauce (without the cornstarch slurry yet) into the skillet. Bring to a gentle simmer, scraping up any browned bits from the bottom of the pan.

Once simmering, re-whisk the cornstarch slurry and slowly pour it into the sauce while continuously stirring. Continue to stir until the sauce thickens to your desired consistency, about 1-2 minutes. It should be thick enough to coat the back of a spoon.

Return the cooked beef to the skillet with the thickened teriyaki sauce. Toss gently to ensure all the beef slices are evenly coated in the glossy sauce.

Serve immediately over hot steamed rice, garnished with sesame seeds and sliced green onions, if desired. Pair with steamed broccoli or your favorite stir-fried vegetables for a complete meal.