Bring a large pot of salted water to a rolling boil over high heat. Add the ditalini pasta and cook according to package directions, usually around 8-10 minutes, until al dente. Before draining, remember to reserve 3 cups of the starchy pasta water.

In a large deep skillet, heat 2 tablespoons of olive oil over medium heat. Once hot, add the finely chopped shallot and onion. Sauté for about 4-5 minutes until softened and fragrant but not browned.

Stir in the fresh or frozen peas and 2 cups of the reserved pasta water. Increase the heat slightly and simmer for 5-8 minutes, allowing the peas to tenderize.

Gently fold the drained pasta into the skillet. Mix well, adding reserved pasta water if a soupier consistency is desired. Let everything simmer together for about 3 minutes.

Remove from heat and stir in 1 cup of freshly grated Parmesan cheese. Season with salt and pepper to taste and serve warm, topping with extra cheese.