Cook noodles in boiling water until chewy-tender, 6–7 minutes. Drain, rinse cool, and snip shorter with scissors.
Whisk soy sauce, brown sugar, sesame oil, and black pepper in a bowl until the sugar dissolves.
Heat 1 tbsp canola oil in a large skillet over medium-high. Sear beef until just cooked, 2–3 minutes. Transfer out.
Add remaining oil. Stir-fry onion and mushrooms 3 minutes. Add carrots and bell pepper; cook 2 minutes.
Stir in garlic for 30 seconds. Add spinach and wilt briefly. Return beef to the pan.
Add noodles and sauce. Toss over heat until glossy and coated, 1–2 minutes. Fold in scallions and sesame seeds.
Taste and adjust seasoning. Serve hot, adding a drizzle of sesame oil if desired.