Cook the soba noodles according to package directions—usually about 4 minutes until tender but still firm. Drain and rinse under cold water to stop the cooking. Toss with a tiny pinch of salt to prevent sticking, then set aside. (Tip: overcooking is the most common mistake here; they'll soften more when you stir fry them later.)
Prepare the sauce by whisking together soy sauce, oyster sauce, rice vinegar, sesame oil, cornstarch, brown sugar, water, and grated ginger in a small bowl until smooth. Set aside.
Season the steak strips with salt and pepper, then heat olive oil in a large skillet or wok over medium-high heat (about 2 minutes). When the oil shimmers, add the beef in a single layer—if your pan is crowded, cook in two batches. Sear for about 90 seconds per side until browned but still pink inside. The internal temperature should reach 135°F for medium-rare or 145°F for medium. Remove to a plate and tent loosely with foil.
In the same pan, add neutral oil and increase heat to high. Add broccoli florets first—they need the most time—and stir-fry for 2 minutes. Push them to the side, then add bell pepper strips. Cook another minute until bright green and slightly tender-crisp.
Return the steak (with any juices on the plate) back to the pan along with the sauce mixture. Stir constantly for about 30 seconds—the cornstarch will thicken the sauce quickly—until everything is coated and steaming.
Add the cooked soba noodles, tossing gently to distribute evenly without breaking them up further. Cook another minute until heated through and glossy from the sauce.
Taste and adjust: add a pinch more salt if needed, or a splash of soy sauce for deeper flavor. Serve immediately, garnished with toasted sesame seeds and sliced green onion.