Add 1 cup of the simmering stock and cook, stirring constantly with a wooden spoon, until all of the liquid has been absorbed by the rice, about 5 minutes. As each addition is absorbed, continue stirring and adding stock, 1/2 cup at a time, until the rice is tender but still al dente. You should begin tasting the rice after it has cooked for about 20 minutes. Just before the rice is ready, stir in the reserved asparagus tips, 1/2 cup of the cheese and the parsley. Season with salt and pepper.