Cook the pasta according to the package directions.
Meanwhile, add the Parmesan, avocados, lemon juice, olive oil, and garlic, if using, to a food processor or blender. (I grate the garlic into the bowl of the food processor or blender on a microplane to ensure it gets thoroughly combined.)
Blend smooth, stopping to scrape down the sides of the bowl a few times until very smooth. Taste and adjust the lemon juice and salt.
Stir the avocado sauce into the pasta, starting with a little and adding more to coat the pasta.
Serve warm or at room temperature as a pasta salad. Season to taste with salt as needed and extra Parmesan.
