In a food processor, combine the basil, garlic, pine nuts, Parmesan, and a pinch of salt. Pulse until everything is finely minced, stopping once or twice to scrape down the bowl. With the machine running, pour the olive oil through the feed tube in a slow, steady stream and blend until the mixture turns creamy.
Spoon the pesto into a medium bowl, fold in the heavy cream, then taste and add a little more salt if needed. Serve as desired.
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Notes
If you're not using the pesto right away, transfer it to a bowl and refrigerate. Press a piece of plastic wrap directly against the surface to help keep its bright green color.
One batch makes roughly 1 ½ cups pesto—about 12 fluid ounces.