Add 1/4 cup toasted pine nuts, 1 garlic clove, and 2 tablespoons lemon juice to a food processor and pulse until finely chopped.
Add 2 cups packed basil leaves and 1/3 cup grated Parmesan to the processor and pulse until the basil is finely chopped.
With the processor running on low, slowly drizzle in 1/3 cup extra virgin olive oil until the pesto is smooth, scraping down the bowl as needed; set aside.
Cook 20 ounces cheese tortellini according to package directions until al dente, then drain and rinse briefly under cold water until no longer warm.
Transfer the cooled tortellini to a large bowl and add enough pesto to coat the pasta; stir gently to combine.
Add 1½ cups fresh arugula, 1 cup halved cherry tomatoes, 1 cup small mozzarella balls, and remaining 1/4 cup toasted pine nuts; toss gently and season with salt and pepper to taste.
Garnish with fresh basil and serve immediately or chill as desired.