In a large bowl, combine soy sauce, 1 teaspoon oil, 2 teaspoons cornstarch, and honey.
Cut Flank steak lengthwise in half. With knife held in slanting position, almost parallel to the cutting surface, cut each half of steak crosswise into ⅛-inch thick slices. Add meat to soy mixture; toss to coat. Cover and refrigerate for 30 minutes.
Cut broccoli into small florets. With a vegetable peeler; peel broccoli stems; cut into ⅛-inch thick slices.
In a nonstick 12-inch skillet or wok, heat 1teaspoon oil over high heat. Add broccoli florets and stems and cook, stirring frequently (stir-frying), 1 minute. Add ¼cup water. Cover and cook 2 minutes; remove cover and cookie, stir-frying, until water has evaporated, about 2 minutes longer. Transfer to large bowl; keep warm. Wipe skillet with paper towels.
In a skillet, heat 1 teaspoon oil over high heat until very hot. Add half of the beef and stir-fry until browned, about 3minutes, transferring meat as it is browned to bowl with broccoli. Repeat with 1 teaspoon oil and remaining beef.
In a small bowl, blend the remaining 1teaspoon cornstarch and 1 tablespoon water until smooth; set aside. Heat the remaining 1 teaspoon oil in a skillet over high heat until hot. Add ginger, garlic, and crushed red pepper; cook 30seconds. Stir in remaining ⅓ cup water and oyster sauce; heat to boiling. Stir in cornstarch mixture. Stir-fry until sauce has thickened and boils. Stir beef and broccoli into sauce in pan; heat through. Transfer to warm platter.