Freeze steak for 30 minutes until partially frozen. Slice steak against the grain, on the diagonal, into 8 equally thin pieces. Use a meat mallet to pound each piece of meat to 1/8 inch thick. If using thin sliced sirloin, skip this step.
Combine marinade ingredients in a bowl and add meat slices. Let stand 15 minutes to 2 hours.
In a separate bowl, combine sauce ingredients.
To prepare filling, heat a wok or skillet over high heat. When hot, add vegetable oil, swirling to coat the sides. Add garlic and ginger and fry for 20 seconds. Add carrot, bell pepper, celery and stir fry for 1 minute. Add soy sauce, sesame oil and stir. Transfer to bowl and let cool.
To make the beef rolls, lay beef slices out with short side facing you. Equally divide chives, enoki mushrooms and vegetable mixture among the pieces of meat. Roll the beef up, over the filling and secure with toothpick.
Place a large skillet over medium-high heat. Add the vegetable oil and butter, swirling to coat bottom. When hot, add beef rolls, seam side down, not touching and pan fry for 1 minute, turn roll. Add sauce to the pan. Cover and simmer over medium heat until beef is just cooked through, 1-2 minutes. Remove toothpick, sprinkle with sesame seeds to serve.