Slice the beef thin and across the grain: pat the flank steak dry, slice across the grain into strips about 1/4 inch thick. Toss with salt and pepper, then with cornstarch until every piece has a thin, even coating. Let sit while you mix the sauce.
Mix the sauce: stir together the soy sauce, water, and brown sugar until the sugar dissolves. Set near the stove.
Sear the beef in batches: heat a wok or large skillet over high heat until it just starts to smoke. Add 2 tablespoons oil and swirl. Add half the beef in a single layer, let sit undisturbed 1 minute, then stir-fry 1 to 2 minutes until browned and crisp at the edges. Move to a plate and repeat with remaining beef, adding the last tablespoon of oil if needed.
Build the sauce: lower heat to medium. Add scallion whites, garlic, ginger, and pepper flakes if using. Stir 30 seconds until fragrant. Pour in the sauce and simmer 1 to 2 minutes until slightly thickened and glossy.
Bring it together: return beef and any juices to the pan. Toss 1 minute until coated. Add scallion greens and sesame oil and toss once more. Remove from heat.
Serve over hot rice, scattered with sesame seeds if you like.