1. Insert the chopping blade into the work bowl of the food processor. Add the garlic and shallot and pulse to chop, about 5 times. Scrape down the sides of the bowl and pulse another 2 to 3 times. Add the chickpeas, salt, pepper, spices, parsley and 1 tablespoon of flour. Pulse 10 to 12 times to coarsely grind the chickpeas. Scrape down the sides of the bowl and then process on Low for 10 to 15 seconds until finely ground.
2. Dissolve the baking soda in the tablespoon of water and with the unit running on Low, pour through the feed tube. Process for 15 to 20 seconds to blend well.
3. Using a tablespoon measure, scoop chickpea mixture and shape into 15 balls. Place the balls on a tray or plate lined with wax paper and chill in the refrigerator for 30 minutes. Put the remaining ½ cup of flour in a shallow bowl and set aside.
4. Fill a 3-quart saucepan with enough oil to reach ¼-inch depth and place over medium-high heat until an inserted thermometer registers 375°F.* Roll the falafel in the flour, shaking off any excess and drop into the oil. Cook the falafel in batches, no more than 5 at a time, for about 2½ to 3 minutes, turning halfway through until browned and crisp.
5. Remove to a paper towel-lined sheet tray and repeat with remaining falafel.
6. Serve falafel with sliced pita, veggies and a drizzle of tahini.
*If choosing to bake instead: Preheat oven to 400°F. Line a baking sheet with parchment and drizzle with olive oil. Skip the step of coating the falafel in flour and arrange on the parchment. Drizzle with more oil, turning to coat the balls all over. Bake for 20 to 25 minutes, turning halfway through until browned and crisp.