To a large ziptop bag, add the steak and cornstarch. Seal and toss to coat. Set aside while preparing the sauce.

To a medium saucepan, add 1 tablespoon olive oil, 1 tablespoon sesame oil, garlic, and ginger. Heat over medium-high for about 1 minute, or just until garlic is fragrant, taking care not to scorch it.

Add the soy sauce, water, and brown sugar. Stir until the sugar has dissolved. Bring to a boil and allow it to boil for about 2 to 3 minutes. Then reduce the heat to low and simmer for about 5 minutes, or until slightly thickened and reduced. While it simmers, sear the steak.

To a large skillet, add the remaining 2 tablespoons olive oil, 1 tablespoon sesame oil, and the steak. Cook over medium-high or high heat until steak is cooked through, about 5 to 7 minutes, flipping the pieces intermittently to ensure even cooking.

Add the broccoli.

Evenly drizzle in the soy sauce mixture, noting it will bubble up dramatically. Toss the beef and broccoli to coat evenly with the sauce. Simmer for about 3 to 5 minutes at medium-high, or until the broccoli is as crisp-tender as desired.

Optional: If your sauce hasn't thickened up as much as you'd like and your broccoli is done or nearly done, and you want a sauce that clings better and isn't as thin, simply dissolve 1 tablespoon cornstarch in 1 tablespoon water (called a slurry), add it to the skillet, and stir for about 1 minute, or until your sauce has thickened to your desired level. Since 6 cups of broccoli were used, the natural water and juices that escaped from it thinned out the sauce, so a slurry was needed.

Turn off the heat, add the green onions, and stir to incorporate.

Optionally, evenly sprinkle with red pepper flakes (makes the dish taste more authentic and gives flavor without adding much heat), optional sesame seeds, and serve immediately.