Snap off the tough ends of the asparagus and set aside. Peel the spears halfway up and cut in pieces. Do not discard the peelings.
In a saucepan, place the tough ends of the asparagus, the peelings and the chicken stock and bring to a boil. Reduce the heat, cover and simmer 15 minutes to flavour the stock. Strain the stock and return to the saucepan. Cover and keep warm over very low heat.
In a large, heavy-bottomed saucepan, sweat the onion, celery and carrot in the butter. Add the rice and stir well to coat each grain with butter. Add the wine and continue cooking until it has evaporated.
Add 125 ml (1/2 cup) of stock and cook, stirring constantly, until it is absorbed. Repeat until there is only 250 ml (1 cup) of stock left. Add the asparagus pieces and remaining stock to the pan and stir until it is absorbed. Season to taste and stir in the cream. At the last minute, stir in the grated parmesan.