Cut flank steak into 2-inch wide strips with the grain then sliced into thin 1/4-inch thick pieces against the grain.
In a medium mixing bowl whisk together 1 Tbsp soy sauce with 1 tsp cornstarch. Toss steak strips with soy sauce mixture, let rest 15 minutes while you chop and prepare remaining ingredients.
In a mixing bowl whisk together 2 Tbsp soy sauce with 1 1/2 Tbsp cornstarch. Stir in chicken broth, honey, rice vinegar and sesame oil, set aside.
Heat 1 Tbsp oil in a 12-inch non-stick skillet over medium-high heat. Dab steak pieces dry with paper towels*.
Scatter half of the steak across pan then let cook until browned on bottom, about 1 1/2 minutes, flip and cook opposite side until browned on bottom, about 1 to 1 1/2 minutes. Transfer to a plate leaving oil in pan (if needed add in a little more oil) and repeat with remaining half of steak.
Heat remaining 1 Tbsp oil in skillet over medium-high heat, add green onions, garlic and ginger, saute 30 seconds. Toss in broccoli and water, reduce heat slightly, cover and let steam until tender crisp, tossing occasionally, about 4 - 5 minutes.
Whisk soy sauce mixture once more then pour into skillet. Cook and toss until sauce has thickened, about 1 minute (careful not to cook too long or moisture in broccoli will break down into sauce and thin it).
Toss in steak, season with a little more soy sauce if needed. Serve warm over rice if desired garnished with sesame seeds or red pepper flakes.