Mix the marinade/sauce in a medium bowl by combining soy sauce, oyster sauce, rice vinegar, honey, sesame oil, cornstarch, and water. Whisk until smooth with no cornstarch lumps.
Place the beef strips in a bowl and add 3 tablespoons of the marinade mixture. Toss to coat and set aside for at least 5 minutes while you prepare the other ingredients.
Bring a large pot of water to boil and cook the soba noodles according to package directions, usually 4-5 minutes. Be careful not to overcook – they should be just al dente. Drain and rinse with cold water to stop the cooking process.
Heat 1 tablespoon oil in a large skillet or wok over high heat until shimmering. Add beef in a single layer (working in batches if necessary) and cook for 2-3 minutes until browned but still slightly pink inside. Remove to a clean plate.
Add another tablespoon of oil to the same pan and add broccoli. Stir-fry for 3 minutes until bright green but still crisp. Add bell pepper if using and stir-fry for 1 minute more.
Lower heat to medium and add remaining tablespoon of oil along with minced garlic, grated ginger, and white parts of green onions. Stir constantly for 30 seconds until fragrant.
Return beef to the pan and add the remaining sauce. Stir well and let the sauce bubble and thicken for about 1 minute.
Add the cooked noodles to the pan and toss everything together until well coated with sauce and heated through, about 2 minutes.
Serve immediately garnished with sesame seeds, green onion tops, and cilantro if desired.