Whisk soy sauce, water, brown sugar, garlic, ginger, sesame oil, and red pepper flakes; set aside.
Pat steak dry, then toss with cornstarch until evenly coated; shake off any excess.
Heat 2 tablespoons oil in a large skillet or wok over medium-high heat.
Sear half the beef until browned, about 2 minutes; transfer to a plate.
Add remaining oil and cook the rest of the beef the same way.
Pour off extra fat, leaving about 1 tablespoon in the pan.
Stir in the sauce; simmer, stirring, until slightly thickened, 2 to 3 minutes.
Return beef and accumulated juices; toss until coated and glossy, 1 to 2 minutes.
Fold in green onions; cook 30 seconds, then serve over rice.