Bring a large pot of water to a boil, salt it, add the pasta and cook until al dente. Drain, reserving 1 cup pasta cooking water.
While the pasta is working, using a food processor, combine the sun-dried tomatoes, garlic, crushed red pepper and 2 tablespoons hot water. With the machine on, drizzle in the EVOO. Add the grape tomatoes, salt and lots of pepper and process until smooth. Transfer the sauce to a large, shallow bowl and stir in the cheese and most of the parsley and chives.
Stir in the reserved pasta cooking water, then add the pasta and toss vigorously for a minute or 2. Scatter the remaining herbs on top.