Add the avocado, buttermilk, mayo, vinegar, sour cream, garlic, lime juice, salt, and pepper to a blender or food processor. Cover and puree until smooth. Scrape down the sides as needed.
Pour dressing into a mason jar.
Add the parsley and chives to the jar. Cover and shake to combine.
Taste the dressing and add more salt and pepper if needed.
Refrigerate in an airtight container until ready to serve.