In a small bowl, whisk the soy sauce, water, brown sugar, sesame oil, red pepper flakes, ginger paste, and cornstarch until combined. Set the sauce aside.
In a 10-inch skillet, heat 1/2 tablespoon of oil over medium-high heat until it’s hot, but not smoking. Rotate the pan to ensure the oil evenly coats the bottom of the pan. Adjust the heat to medium and add the broccoli to the pan. Cook it in the oil, stirring frequently, until it’s crisp-tender, about 3 to 4 minutes. Transfer the broccoli to a plate and set aside.
Add 1/2 tablespoon of oil to the same pan. Once it’s heated, add the sliced entreecanto in an even layer. Cook the beef for 1 to 2 minutes on each side. Transfer the beef to the plate with the broccoli and set aside.
Pour the sauce into the pan. Simmer the sauce for 2 to 3 minutes, or until it thickens. Add the broccoli and beef to the pan and stir to coat it in the sauce. Cook them in the sauce for a minute or so. Serve with the cooked white rice.