Toss sliced beef with soy sauce and cornstarch. Set aside.
If needed, briefly blanch noodles until just tender. Drain well and let dry.
Heat 2 tablespoons oil in a wide skillet over medium-high heat. Spread noodles in an even layer.
Cook undisturbed until the bottom turns golden and crispy. Flip gently and crisp the other side. Remove and set aside.
Add remaining oil to the pan. Sear beef quickly until just cooked. Remove from pan.
Add garlic, ginger, cabbage, and carrots. Stir-fry 1–2 minutes until just tender.
Whisk sauce ingredients together and pour into the pan. Bring to a light simmer.
Return noodles and beef to the pan. Toss gently until evenly coated.
Remove from heat, drizzle with sesame oil, garnish with green onions, and serve immediately.