Bring a large pot of salted water to a boil. Cook fusilli according to package directions until al dente. Drain, then rinse under cold water until cool to the touch. Drain well and set aside.
In a food processor, combine basil leaves, pine nuts, garlic, Parmesan, lemon juice, and salt. Pulse until finely chopped. With the motor running, slowly drizzle in the olive oil until a smooth, emulsified pesto forms. Scrape down sides as needed.
In a large mixing bowl, toss the cooled pasta with the pesto until every piece is well coated. Gently fold in halved cherry tomatoes and mozzarella pearls.
Just before serving, fold in the baby arugula until evenly distributed. Garnish with toasted pine nuts and fresh basil leaves.