In a food processor or blender combine 2 avocados, buttermilk, green onion, parsley, mint, lemon juice, water, and salt and pepper. Pulse until smooth. This will keep for up to 3 days in the refrigerator.
In a medium bowl combine chicken, celery, shallot, 1 avocado, mayonnaise, dry ranch dressing, and parmesan cheese. Season with salt and pepper and toss to combine. Serve on toasted sourdough bread. You can use the leftover avocado dressing for a spread on the sandwiches.