Trim at least 1 in (2.5 cm) from the tough ends of the asparagus to reach the moist part. Peel, then wash.
In a pan where the spears can lie flat, add water to about 2 in (5 cm) up the sides and add 1 tbsp salt (15 ml). Boil, add asparagus, cover, and cook 4 to 5 minutes after the water returns to a boil. Drain, saving the cooking water, and let asparagus cool.
Cut off the tips about 1 1/4 to 1 1/2 in (3 to 4 cm) from the top and reserve. Cut the remaining stalks into 1/2 in (1.5 cm) pieces, discarding any very tough bottoms.
Add enough broth to the asparagus water to make about 6 cups (1.4 L). Keep it at a very slow, steady simmer near the risotto pot.
In a broad, sturdy pot over medium-high heat, cook onion in 1 tbsp butter and the oil until translucent. Add the cut asparagus stalk pieces (not the tips) and stir about 1 minute to coat.
Add the rice and stir until coated. Add 1/2 cup (120 ml) simmering liquid and continue cooking as for basic risotto, adding liquid as needed.
Cook until the rice is tender but firm, with barely enough liquid left for a somewhat runny consistency. Off heat, stir in asparagus tips, pepper, remaining butter, all the Parmesan, and parsley. Taste and correct for salt, then serve.