Bring a large pot of salted water to a boil.
While you wait, whisk together the oil, vinegar, and red pepper flakes in a large bowl (choose something that can accommodate the sauce and the pasta). Finely grate the garlic into the mixture.
Use a mortar and pestle to smash the anchovies into a paste (or use a knife to mince, then smash the anchovies into a paste on your cutting board). Scrape the anchovies into the bowl and whisk again to combine.
Halve the tomatoes and toss into the dressing. Finely chop the onion, parsley, and basil; add to bowl. Squeeze the thyme sprigs in your palms until you can smell the essential oils being released, then add the whole sprigs to the mixture.
Use your hands to tear the mozzarella into ½-inch irregular pieces and add to the dressing; stir to coat everything and season again with salt and pepper. Let tomato-mozzarella mixture sit while you cook the pasta, or cover and let sit at room temperature for up to 6 hours, stirring occasionally.
Cook the pasta a minute or two less than al dente; as it sits and absorbs the dressing, it will soften, and we don’t want gummy noodles. Reserve about a cup of pasta cooking liquid, then drain and add to tomato-mozz mixture. Do. Not. Rinse.
The warm pasta will enhance the deliciousness of the tomatoes and melt the mozz, and the dressing will be absorbed better into the noodles when they’re hot. Remove the thyme sprigs from the sauce.
Add the pasta to the bowl and gently stir and toss until the pasta is well coated with the sauce and the mozzarella has started to melt into strings. Taste and season with additional salt, pepper, and/or pepper flakes, as needed.
Let pasta salad cool, tossing occasionally, until it’s room temperature and the pasta has softened that last little bit. Add the blender parm and stir gently to combine. Enjoy on hot nights, on picnic blankets, out of beach bags, at music festivals, or while standing at the kitchen counter.
