In a food processor, combine everything but the jalapeños and olive oil. Blend until the ingredients are finely chopped, pausing to scrape down the sides as necessary. Add the jalapeños and pulse until the peppers are finely chopped, but not completely obliterated.
Stir the olive oil into the sauce by hand, and transfer to a bowl for serving. If the sauce is outrageously spicy at first, give it a 30-minute rest—it usually mellows out a bit. This sauce keeps well in the refrigerator, covered, for 1 to 2 weeks.
Recipe Notes
MAKE IT NUT FREE: Substitute pepitas for the walnuts.