The afternoon before you want to make the falafel, soak the rinsed dry chickpeas in a bowl of water. Make sure the chickpeas are covered by a couple of inches of water and put keep them in the refrigerator.
First, make the Lemon Tahini Sauce: Place the tahini in a bowl. Stir it well. Stream in the water, whisking constantly. Add the rest of the ingredients and mix well.
The next day, drain the chickpeas and put them in a food processor, along with the rest of the falafel batter ingredients. Process until everything is creamy, scraping down the sides of the bowl. Form each tablespoon of mixture into a one inch pattie. Place the patties on waxed paper.
In a Dutch oven, heat an inch and a half of oil to 375 degrees. Fry in about four batches, until the falafel is brown all over. You will have to flip them over, so they brown evenly. Do not add more oil until the oil comes back to 375 degrees. Drain the falafel well.
Serve the falafel on top of or inside of the bread, with the sliced vegetables and Lemon Tahini Sauce.