In a bowl, whisk together ingredients for the marinade. Add beef and toss to coat evenly. Cover with plastic wrap and let marinade for at least 10 minutes.
Heat 1 teaspoon olive oil in a large non-stick pan over medium heat. Add beaten eggs and cook until firmly set. Fold in half and remove from the pan; cut into long thin strips. Set aside.
Using the same pan, heat 1 teaspoon olive oil over medium heat. Add onion and a pinch of salt; stir fry until soft and translucent. Transfer onion to a large plate.
Repeat step 3 (omitting salt) for carrot, bell pepper and mushroom.
In the same pan, add the seasoned beef and stir fry until browned and all moisture has evaporated. Transfer beef to a plate.
Wash and blanch spinach in boiling water, drain and squeeze the excess water. Season with sesame oil and salt. Set aside.
Cook the noodle in boiling water for 6-10 minutes. Drain well. Drizzle noodles with sesame oil and toss to coat. This step is necessary to avoid noodles sticking together.
In a small bowl, whisk together ingredients for the sauce. Pour over the noodles and toss to coat evenly.
Toss seasoned noodles, beef and vegetables together. Add half of the omelette and gently toss to combine.
Transfer to individual plates. Garnish top with long strips of omelette and a sprinkle of sesame seeds.