In a food processor, blend up the chickpeas, onion, garlic, parsley and cilantro into a thick paste. I had to do this in two batches since my food processor couldn't handle this entire recipe all at once. You'll also notice there is no liquid added, which makes it rather hard to blend. Keep at it and don't add water no matter what! Adding water will likely result in falafel that won't hold together during the frying process.
Once you've blended everything into a paste, spoon it into a large bowl and add the salt, baking powder, flour and pepper. Stir until well combined. Cover with plastic wrap and allow to rest in the refrigerator for 2 hours. If you're in a time crunch you can place it in the freezer for an hour instead. But don't skip this rest period, because it will result in falafel that falls apart when fried.
In the meantime, make your dressing. Stir together the ingredients in a small bowl and allow to set for at least 30-45 minutes before serving so the flavors and blend together.
In a deep fryer or large, heavy pot heat enough oil for the falafel float. You want the oil temperature to reach around 350°F. You can use a candy thermometer to monitor the temperature or you can test it by dropping a little batter in. It should start to bubble/fizzle and the batter should float after a few seconds. Once the oil is ready, drop small balls of the falafel batter in and allow them to cook for 2-3 minutes. Remove from the oil and place on a plate lined with paper towels, to remove excess oil.