Combine all of the ingredients in the bowl of a food processor. Process until the sauce is smooth and the herbs are very finely chopped, about 30 seconds. Taste and adjust seasoning, if necessary. Serve immediately if you'd like the dressing to be a drizzleable consistency, or chill for a few hours until thickened to use a dip. (To bring the dressing back to a drizzleable consistency after chilling, allow it to sit out at room temperature for about an hour and stir well before using.) The dressing will keep well in a covered container in the refrigerator for 4 to 5 days.