Heat the oil in a heavy 3-4 quart (3-4 L) saucepan. Add the onion and sauté over medium-low heat until it is tender but not brown. Stir in the peas and 4 cups (1 L) of the stock.
Simmer uncovered until the peas are very tender, about 30 minutes.
With a slotted spoon, remove half of the peas and reserve. Puree the remaining contents of the saucepan and set aside.
In a clean 3-quart (3 L) saucepan, melt 2 tablespoons (30 g) of the butter.
Add the rice and cook over medium heat until it becomes opaque. Stir in the wine, the remaining stock, and the pureed pea mixture.
Simmer gently, stirring from time to time, for 15 minutes.
Add half the reserved peas, cook 10 minutes longer, then add the remaining peas and the remaining 2 tablespoons (30 g) of butter.
Season with salt and pepper, stir in the Parmesan cheese, and serve in soup plates.