Place chickpeas in a large bowl and mash gently with a potato masher, taking care not to mash too finely.  (Leave some chickpeas whole for added texture).

Add techina, lemon juice, olive oil, fresh parsley, and spices and mix gently to combine.  Adjust seasoning to taste.

Smear one tablespoon of mayonnaise onto the center of each wrap.  Place about half a cup of the chickpea salad on top of the mayo, flattening it down with a spoon.

Divide vegetables evenly among the four wraps, arranging on top of the chickpea salad.  Drizzle generously with additional techina.

Fold the ends of the wraps toward each other over the filling and roll closed.  Slice each wrap in half horizontally to serve.