Heat oven to 400F. Meanwhile, toss together brussel sprouts, olive oil, dried mustard and 1/4 each salt and pepper. Spread sprouts out on a large sheet pan.
Roast for 15 minutes. While brussel sprouts are roasting, season salmon with another 1/4 tsp each salt and pepper. Remove sheet pan from oven and toss and move vegetables making room for salmon. Place salmon on sheet and return to oven.
Roast another 15 minutes. Remove from oven and use a fork to ensure fish flakes easily. Drizzle everything with balsamic vinegar if using. Serve.