Another idea could be salsa verde, so far I have only seen it at Manor, as a short-consumption bulk product, but I can well believe that it could be produced like pesto in jars (In italy there is for example from the Biffi brand). And an excellent sauce to accompany boiled meats and fish, here's the description:
https://www.biffishop.it/salsa-verde-biffi-compra-online.html
and can be used as a substitute for parsley (a bit like pesto replaces basil)