Wash the pea pods; open and remove peas. Set aside.
Place the pea pods in a large pot with carrot, onion, celery and a pinch of salt. Cover with water, and bring to the boil. Reduce heat and simmer for 1 hour. Strain through a sieve and check to see if you have about 700ml of vegetable stock. If not, add some more water. Set aside.
Heat 1 tablespoon olive oil in a large saucepan over medium-low heat; cook the onion and garlic in oil for a few minutes. Add the peas, parsley and 1 tablespoon of stock. Cook on medium-low heat, adding a little stock if necessary, until the the peas have softened. Check every few minutes or so as the cooking time will depend on the quality and freshness of the peas.
Heat up the vegetable stock in a pot. Simmer on low heat.
Once peas are cooked, add the rice and toast for 1-2 minutes, stirring often. As soon as the rice smells fragrant and "nutty", add enough hot stock to just cover the rice. Cook, stirring often, until the rice absorbs the stock; then add more stock, one ladle at the time, stirring often.
Taste the rice 15 minutes after the first batch of stock was added. If it is still hard in the middle, cook for 1 or 2 minutes longer. The cooking time will depend on the quality of rice.
Once the rice is cooked, remove from heat and sprinkle with grated Parmesan. Stir and season to taste. Let stand for a few minutes before serving.