Make the dressing by putting the mayo, basil, lemon juice, and garlic, if using, and a pinch of salt into a small food processor. You can also use an immersion blender.
Process, scraping down the sides of the machine as needed, until the mayo is pale green and smooth. You'll see little flecks of basil in the dressing. Taste to add more salt or lemon juice. Scrape the mayo into a small airtight container and chill. Note: the mayo will thicken as it chills. You can do this a day or two ahead if you like.
Cook the pasta in plenty of well salted water until al dente. Drain and rinse in cold water.
Combine the chilled mayo with the pasta, lemon zest, grated cheese, and toasted pine nuts. Add salt and pepper to taste. Note: For this particular salad I like to wait until the pasta has cooled completely before combining with the chilled dressing so the mayo clings to the penne rather than melting into it.
Chill until ready to serve. I like to add a little more fresh basil right before serving: stack and tightly roll a few leaves, then very thinly slice crosswise into shreds with a sharp knife. The pasta salad will keep for 3-4 days in the refrigerator.