Heat the oven to 425°F (220°C) with a rack in the lower third. Put a large rimmed baking sheet in the oven to heat.
Toss the sprouts with the oil, salt and pepper in a bowl.
Carefully take out the hot pan and arrange the sprouts cut side down in a single layer. Roast for 12 minutes.
Add the apple wedges and nuts to the pan, toss gently and roast 8–12 minutes more, until the sprouts are browned and tender when pierced with a knife.
Whisk the maple syrup and vinegar together, drizzle over the hot vegetables and toss. Taste for salt and add pepper flakes if you like. Serve warm.