Bring a large pot of water to a boil. Cook noodles according to package directions, usually 6–7 minutes until tender. Drain and rinse under cold water. Toss with 1 Tbsp sesame oil to prevent sticking; set aside.

In a small bowl, whisk together soy sauce, sugar, 1 Tbsp sesame oil, and a pinch of salt and pepper. Set sauce aside.

Heat 1 Tbsp vegetable oil in a large skillet or wok over medium‑high. Add garlic and sauté 30 seconds until fragrant.

Add carrot and bell pepper; stir‑fry 2–3 minutes until beginning to soften.

Push veggies to one side, add remaining oil and optional beef. Stir‑fry beef 2–3 minutes until browned and nearly cooked through.

Stir in mushrooms and green onions; cook another 2 minutes.

Add noodles and sauce to pan; gently toss all together and cook 1–2 minutes until everything is evenly coated and heated.

Transfer to a serving platter, sprinkle with sesame seeds, and serve warm or at room temperature.