In the bowl of a food processor or a high-speed blender, combine the parsley leaves, a pinch of salt, the garlic, and about half of the olive oil.
Pulse or blend until the mixture is roughly chopped. Scrape down the sides of the container, then turn the machine on and gradually stream in the remaining olive oil until the purée is smooth.
Add the sherry vinegar or lemon juice and blend for a few more seconds to combine.
Check the consistency. If you prefer a thinner sauce, add a little more olive oil or a tablespoon of water.
Taste and adjust the seasoning with more salt or garlic if needed.
Serve immediately or transfer to an airtight container and refrigerate for up to 3 days.