Sauté the Shallot:
Heat the olive oil in a large, deep pan or Dutch oven over medium heat. Add the finely chopped shallot and sauté for 3-4 minutes until softened and fragrant.
Cook the Pasta:
In the meantime, bring a pot of water to a boil. Salt it generously, then add the pasta and cook it for only half of the time indicated on the package. Before draining, reserve at least 1 litre (4 cups) of pasta water.
Cook the Peas:
Add the peas to the pan with the sautéed shallot. Pour in 1 cup of the reserved pasta water and let the peas simmer for 10-15 minutes until tender.
Combine Pasta and Peas:
Transfer the partially cooked pasta to the pan with the peas. Gradually add more pasta water, stirring frequently, until the pasta is cooked al dente. This should take about 5 minutes, and you should still have some liquid left to create a sauce.
Finish the Dish:
Turn off the heat and stir in the grated parmesan and fresh basil (if using). Season with salt and freshly ground black pepper to taste. Serve immediately, garnished with extra grated parmesan.