Cook noodles in boiling water according to package directions, drain, and set aside.
In a small bowl, whisk together soy sauce, oyster sauce, brown sugar, minced garlic, grated ginger, and cornstarch until smooth.
Heat one tablespoon of vegetable oil in a large wok or skillet over high heat.
Add beef in a single layer and sear until browned, about 2-3 minutes; remove beef and set aside.
Add remaining oil to the wok and stir-fry broccoli and bell peppers for 3-4 minutes until tender-crisp.
Return beef and cooked noodles to the wok.
Pour the sauce mixture over the ingredients and toss constantly for 2 minutes until the sauce thickens and coats everything evenly.
Drizzle with sesame oil and garnish with sliced green onions before serving.