Whisk together the soy sauce, oyster sauce, brown sugar, and sesame oil in a small bowl to create the sweet and savory sauce. Set aside.
Cook the noodles according to the package instructions until al dente. Drain well and set aside.
Heat 1 tablespoon of vegetable oil in a large wok or skillet over medium-high heat. Add the sliced beef and stir-fry for 3 to 4 minutes until browned. Remove the beef from the pan and set aside on a plate.
Add the remaining 1 tablespoon of oil to the wok. Add the minced garlic, broccoli florets, sliced red bell pepper, and snap peas. Stir-fry for 4 to 5 minutes until the vegetables are tender-crisp.
Return the cooked beef and the drained noodles to the wok with the vegetables.
Pour the prepared sauce over the mixture. Toss everything together continuously for 2 minutes, ensuring the noodles, beef, and vegetables are evenly coated and heated through.
Remove from heat, garnish with sesame seeds, and serve immediately.