Bring a large pot of salted water to a rolling boil. Add the pasta and cook according to package directions until al dente. During the last minute of cooking, add the thawed frozen peas to the boiling water to blanch them briefly.

Drain the pasta and peas in a colander. Immediately rinse them thoroughly with cold water to stop the cooking process and cool them down. Set aside to drain completely.

While the pasta cooks, combine the blanched peas, packed arugula, grated Parmesan cheese, toasted pine nuts (if using), minced garlic, and fresh lemon juice in the bowl of a food processor.

Pulse the mixture until finely chopped. With the food processor running, slowly stream in the extra virgin olive oil until the pesto is mostly smooth but still has some texture. Season with salt and freshly ground black pepper to taste. Adjust lemon juice if desired.

In a large mixing bowl, combine the cooled pasta and peas, halved cherry tomatoes, finely diced red onion, and halved or quartered fresh mozzarella balls.

Add the freshly made pea and arugula pesto to the bowl. Toss gently but thoroughly until all ingredients are well coated with the pesto.

Taste the salad and adjust seasonings (salt, pepper, lemon juice) if necessary. Garnish with chopped fresh basil or mint, if desired, before serving.