Marinate the Beef:
In a bowl, combine all marinade ingredients. Add the beef slices and toss well to coat. Cover and refrigerate for 30 minutes (or up to 2 hours for deeper flavor).
Cook the Udon Noodles:
Prepare udon according to package instructions. If using frozen, rinse under warm water to loosen. Drain and set aside.
Stir Fry the Vegetables:
Heat oil in a large skillet or wok over medium-high heat. Add onion, bell pepper, and carrots. Stir fry for 2–3 minutes until just tender.
Cook the Beef:
Push veggies to the side and add marinated beef. Spread it out and let it sear for 1 minute without stirring. Then stir-fry with veggies until fully cooked, about 2–3 minutes.
Add Udon and Sauce:
Add noodles to the pan along with soy sauce and sesame oil. Toss everything together until noodles are coated and heated through, about 1–2 minutes.
Finish and Garnish:
Sprinkle in green onions and sesame seeds. Serve immediately, hot and fresh!