Preheat oven to 220°C/425°F. Add the broccoli, brussels sprouts, panko and parmesan to a large mixing bowl. Drizzle with 1 tbsp of olive oil and season generously with salt and pepper. Mix to combine.
Spread the vegetables over a parchment-lined baking sheet and transfer to the oven. Roast until deeply golden brown and the vegetables are tender but still crisp - about 20 minutes. Serve immediately.