In a 7-cup food processor pulse together 1/2 cup chick peas, the tahini, olive oil, lemon juice, lemon zest, 2 Tbsp reserved chickpea liquid from can, garlic, and season lightly with salt and pepper to taste.
Process until mixture is well blended and practically smooth.
Add remaining chickpeas and pulse several times until partially chopped.
In a large mixing bowl toss together chickpea mixture, bell pepper, celery, red onion, parsley, and tahini mixture. Thin with a little more canned chickpea liquid if needed, season with salt and pepper to taste.
Serve mixture between bread slices with desired toppings. Chill any leftover chickpea salad mixture for up to 3 days.
*I've made this salad two ways and both are delicious. If you are looking for more of a traditional flavor (like tuna salad) then replace the 1/4 cup tahini and 2 Tbsp olive oil with 6 Tbsp vegan mayonnaise or traditional mayonnaise, wait to add the canned chickpea liquid to see if you'd like it thinner.