Pour both cans of chickpeas (and liquid) into medium saucepan. Simmer over medium heat for 10 minutes, then pour chickpeas into colander or sieve and drain well.
Transfer drained chickpeas to large bowl. Using potato masher or fork, mash chickpeas until desired consistency is achieved.
Add celery, onion, parsley, vegan mayonnaise, vegan Dijon mustard, and salt to mashed chickpeas. Stir well to thoroughly incorporate all ingredients.
Chill chickpea salad if desired, or serve immediately on bread or in lettuce cups with preferred toppings.
