Place the steak in the freezer for 15 minutes until firm, then slice it thinly across the grain into strips about 1/8 inch thick.
Toss the sliced beef with cornstarch until lightly coated, then let it sit for 5 minutes.
In a bowl, whisk together the soy sauce, brown sugar, water, rice vinegar, hoisin sauce if using, and red pepper flakes.
Heat a large skillet or wok over medium-high heat, add oil, and sear the beef in batches for 45 to 60 seconds per side until browned.
Remove excess oil, leaving about 1 tablespoon in the pan, then add the garlic and ginger and cook for 15 to 20 seconds.
Pour in the sauce and simmer for 2 to 4 minutes until thickened and glossy.
Return the beef to the pan, toss for 30 to 60 seconds until coated, then add the green onions and toss again.
Serve immediately over rice, with noodles, or with your preferred side.