Begin by cooking the pasta according to package instructions in a large pot of salted boiling water until al dente. Reserve about 1/2 cup of the pasta cooking water, then drain the pasta and set aside.
In a food processor, combine the sun-dried tomatoes, basil leaves, Parmesan cheese, pine nuts, and minced garlic. Pulse until the mixture is coarsely chopped.
With the food processor running, slowly drizzle in the olive oil until the pesto reaches a smooth, spreadable consistency. Season with salt and pepper to taste.
In a large mixing bowl, combine the drained pasta and the sun-dried tomato pesto. If the mixture is too thick, add a bit of the reserved pasta water to loosen it up, stirring until the pasta is well coated.
Serve the pasta on individual plates and garnish with fresh mozzarella balls if using. Sprinkle additional pine nuts and a few basil leaves on top for extra color and flavor.