Preheat oven to 240°C. Place asparagus and capsicum strips in a large shallow baking dish. Drizzle with the oil and toss to coat.
Roast until crisp-tender, 10 to 12 minutes, turning occasionally. Transfer to a serving dish.
Sprinkle with vinegar. Toss to coat. Using a vegetable peeler, shave cheese into thin curls over vegetables. Season with pepper.
Roasted vegetables are an ideal accompaniment for roast meat or poultry. When the roast goes into the oven, prepare the vegetables and place them in a roasting pan with oil and seasonings. When the roast comes out of the oven, turn up the heat and put in the vegetables. They'll have enough time to cook while the roast poultry or meat rests before it's ready to carve. Turn the vegetables once or twice to brown them evenly.