Place the parsley, basil, anchovies, garlic, and vinegar in a blender.
Blend for 2 minutes, scraping down the sides of the container periodically.
With the blender on low speed, slowly add the olive oil in a thin stream, adding a little at a time so that a smooth emulsion forms.
When all the olive oil has been added, blend for 1 minute, or until the sauce is relatively smooth and emulsified.
Season with salt and pepper.
The sauce can be stored in a tightly sealed container in the refrigerator for up to 2 weeks.