Drain and rinse both the fava beans as well as the chickpeas. Combine both beans in the bowl of a food processor, along with the onion, parsley, cilantro, garlic, cumin, baking soda, salt, ground coriander, and cayenne, and pulse, scraping down the sides of the bowl as necessary, until a coarse paste is formed. Add 1 or 2 tablespoons of water, if needed to make the paste hold together - you will have to remove the lid of the processor and check this by pressing some of the mixture together between your fingers. Add a bit more water, if necessary. Transfer to a bowl and set aside to rest for about 30 minutes.
Preheat at least 3-inches of oil in a saucepan or a deep-fryer to 350 degrees F.
Scoop the fava-chick pea mixture into 1 1/2 to 2-tablespoon increments and, using your hands, shape into balls or patties about 1 1/2 to 2-inches in diameter. Gently lower the falafel balls into the hot oil (these are fragile - do not drop them or they will fall apart.) Fry the falafel in batches until crisp and brown, turning to promote even browning, 2 to 2 1/2 minutes. Transfer to paper-lined plates to drain briefly before serving with the Tahini Sauce and pita bread, if using.
Make the sauce by combining the tahini paste, lemon juice, and garlic in a bowl and stirring to combine. Add the water a little at a time as needed to form a smooth, creamy sauce approximately the thickness of heavy cream. (Note that the sauce might appear to separate for a bit before enough water has been added; just keep adding more water bit by bit and stirring until the sauce comes together.) Season to taste with salt and more lemon juice, if necessary. Transfer to a nonreactive container and refrigerate until ready to serve the falafel.
if you cannot find skinless fava beans, you will need to peel them. This is most easily accomplished after the beans have soaked for a short while - the skins will puff up away from the bean and can then be peeled off. While this is not terribly difficult to do, it is very time consuming and we recommend using skinless if you can source them.
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