Remove the outer skins on the chickpeas by squeezing with your fingers or rubbing between towels. This step is optional but yields the best texture. Place peeled chickpeas in a medium bowl.
Mash the chickpeas with the back of a fork until chunky.
Add the vegan mayo, mustard, celery, herbs, onion, salt, and pepper to the bowl of chickpeas. Stir to combine. Taste and adjust seasonings as desired.
Toast the buns. To assemble the sandwiches, fill the buns with a piece of lettuce and the chickpea salad.
Store any leftover chickpea salad in the refrigerator.
Notes
If you don't like mayo, you can sub smashed avocado.