Rinse and dry the vegetables. Chop the cucumber, onion, and celery finely, and mince or very finely chop the garlic.
Add all of the ingredients except half of the parsley into a mixing or salad bowl. Mix until everything is well coated with the mayonnaise and avocado. Taste and adjust the flavor to your liking with salt and pepper.
Garnish with fresh parsley and serve.
The salad will keep well in the refrigerator for up to 5 days in an airtight container.