If you need to grate the Parmesan, do that first, using your food processor or blender, if desired. Measure out 1 ½ cups and set it aside.
Fill a large pasta pot just over halfway with water, add about a teaspoon of salt, and put it on the stove over high heat, covered.
In a food processor or blender, add the drained sun-dried tomatoes, garlic, vinegar, salt and pepper. Pulse a bit to break up the tomatoes. Drizzle in the olive oil as you pulse to combine everything. It's best to wait to adjust the seasonings until after the dressing is stirred into the pasta salad, since the cheese and olives will be salty.
When the water boils, add the pasta to the pot and give it a stir. Cook uncovered, until al dente, stirring occasionally to prevent sticking. (Check it for doneness three minutes before the al dente time listed on the package.)
While the rotini is cooking, rinse your tomatoes, pat them dry, and slice them in half. Drain, rinse, and pat dry your olives. Rinse your basil leaves, roll them up, and slice them into ribbons.
When the pasta is cooked, drain it in a colander in the sink. Transfer the pasta to a large serving bowl and stir in the sun-dried tomato dressing. Add the Parmesan, tomato halves, olives, and basil and stir to combine. Refrigerate the pasta salad, covered, until serving time.
The pasta salad is best at room temperature after it has had time to marinate for a few hours. Stir it again before serving. Store leftover pasta salad in the refrigerator for up to four days. Do not freeze it, because the fresh tomatoes will get mushy.
The sun-dried tomato dressing can be made a 1-2 days ahead of time and refrigerated. If you wish, you can assemble the pasta salad and refrigerate it the day before you serve it. Once made, it should keep for four days.