Slice the top quarter off each head of garlic, exposing the inner cloves. Wrap in foil and roast until soft, about 45 minutes. Open the foil packet and let stand until cool enough to handle.
Meanwhile, place sun-dried tomatoes in a medium bowl. Cover with boiling water and let soak until soft, about 20 minutes. Using a slotted spoon, transfer the tomatoes to a food processor or large blender. Add 6 tablespoons of the soaking liquid, cheese, oregano, oil, vinegar, red pepper and salt. Squeeze in the roasted garlic. Pulse a few times, then process until smooth, or to the desired consistency, scraping down the sides occasionally.