Green Minestrone

Name: Green Minestrone
Ingredients: 6 tablespoons olive oil, divided; 1 leek, white and pale-green parts only, chopped; ½ small fennel bulb, finely chopped; ½ small yellow onion, finely chopped; 2 celery stalks, thinly sliced; 4 cups low-sodium vegetable or chicken broth; 2 small carrots, peeled, thinly sliced lengthwise on a mandoline; 1 cup fresh shelled peas or fava beans (from about 1 lb. pods) or frozen; Kosher salt and freshly ground black pepper; ½ cup fregola, ditalini, or other tiny pasta; 1½ cups (lightly packed) fresh flat-leaf parsley leaves; ½ shallot, finely chopped; 2 red pearl onions or ¼ small red onion, thinly sliced; Shaved Parmesan (for serving)