In a blender, put the roasted red peppers (drained), basil leaves, and garlic cloves. Pulse a few times to get ingredients chopped together. It does not have to be smooth at this point.
Add the balsamic vinegar, rice vinegar, and salt. Pulse a few more times.
Add the grated Parmesan cheese. Blend on medium speed.
With the blender running, slowly add the olive oil. Continue blending until mixture is well blended.
Prepare pasta according to package directions. Be sure to take pasta only to the al dente stage. It will absorb more moisture from the pesto.
Drain pasta, leaving about 1/4 cup of cooking water in the bottom of the pot. Return pasta to pot. Add pesto to the pasta and toss well to coat.
Serve immediately and pass more grated Parmesan for sprinkling on top of pasta, if desired.