Marinate the Beef: Slice steak against the grain into thin strips about ¼ inch thick. Place in a bowl with soy sauce, sesame oil, and white pepper. Mix thoroughly and marinate for 10-15 minutes.
Prepare the Sauce: In a small bowl, whisk together ketchup, honey, rice vinegar, dark soy sauce, brown sugar, chili flakes, and water until smooth and glossy. Set aside.
Coat the Beef: Add beaten egg to marinated beef and mix until every strip is coated. In a separate large bowl, spread cornstarch and season with pinch of salt. Add egg-coated beef strips and toss until completely covered with no wet patches. Shake off excess cornstarch and separate any stuck pieces. Let rest 2-3 minutes.
Fry the Beef: Heat vegetable oil in wok over high heat until shimmering. Test with small piece—it should sizzle immediately. Working in batches, add beef strips in single layer without crowding. Fry 2-3 minutes without moving to develop golden crust. Flip and fry another 2-3 minutes until deeply golden and crispy. Transfer to paper towel-lined plate. Repeat with remaining beef.
Stir Fry Vegetables: Remove most oil from wok, leaving about 1 tablespoon. Add bell pepper, carrot, fresh chilies, garlic, and ginger. Stir-fry over high heat for 30-60 seconds until fragrant but still crisp.
Combine and Serve: Pour prepared sauce into wok and let bubble vigorously for 30 seconds. Add crispy beef and toss quickly for just 10-15 seconds to coat. Immediately transfer to serving plate. Garnish with spring onions and sesame seeds. Serve hot with rice or noodles.