Bring a large pot of salted water to a boil. Cook pasta according to package directions.
Meanwhile, blend the sun-dried tomatoes with olive oil, basil, and garlic in a food processor; pulse into a pesto-like consistency (If it’s too thick, add a little pasta water). Do not finely puree, you want a bit of texture in this dish. Transfer the pesto to a large bowl; stir in Parmesan cheese.
Drain the pasta water, reserving 1 cup of the cooking liquid. Add pasta back to the pot and stir in tomato pesto; toss to coat, season with salt and pepper to taste. Add some of the reserved pasta water, if needed.
Serve immediately with additional fresh basil and Parmesan cheese, if desired. Store any leftover pasta in the refrigerator for up to 3 days.