Cut the beef against the grain into 0.5 cm, or 1/4 inch, slices or into 1 cm, or 1/2 inch, strips. Place it in a small bowl. Add the soy sauce, peanut oil, and cornstarch. Gently toss by hand until each piece is lightly coated in the sauce. Let it marinate for 10 minutes while you prepare the remaining ingredients.
Combine all the ingredients for the sauce in a medium-sized bowl. Mix well.
Pour 1/4 cup of water into a large nonstick skillet and place it over medium high heat. Once the water starts to boil, add the broccoli and cover the pan. Steam for about 1 minute, just until the broccoli is tender and the water has evaporated. Transfer the broccoli to a plate. If any moisture remains in the pan, carefully wipe it out with a paper towel using tongs.
Add the oil to the pan and swirl it around to coat the bottom evenly. Heat over medium high until the oil is hot. Lay the steak in a single layer and let it cook undisturbed for about 30 seconds, until the underside is browned. Flip and cook the other side for a few seconds. Then stir and continue cooking until the outside is lightly charred while the center remains slightly pink.
Add the garlic and ginger. Stir a few times to release the flavor and fragrance.
Add the broccoli back into the pan. Stir the sauce once more to fully dissolve the cornstarch, then pour it into the skillet. Cook while stirring for about 1 minute, until the sauce thickens and coats everything evenly. Transfer to a serving plate right away and serve hot as a main dish.
