The night before, place chickpeas and split fava beans in separate bowls and cover with cold water by at least 3 inches. Soak 12 to 16 hours; the beans will roughly triple in size.

Drain the soaked beans thoroughly. In a food processor, pulse the chickpeas, favas, onion, garlic, parsley, cilantro, chili, cumin, coriander, salt, and pepper in short bursts, scraping down the sides, until the mixture looks like wet coarse sand. It should hold together when squeezed but still show individual specks. Do not process to a smooth paste.

Transfer the mixture to a bowl, cover, and refrigerate at least 30 minutes and up to 4 hours. Chilling helps the paste bind.

Just before shaping, sprinkle the baking soda over the paste and mix gently to incorporate. This is what gives falafel its light interior.

Scoop 2 tablespoons of paste at a time and shape into slightly flattened balls (about 30 g each). If using sesame seeds, press one side of each ball into the seeds. Arrange the shaped falafel on a parchment-lined tray.

Heat 2 to 3 inches of oil in a deep, heavy pot to 350 F (175 C). A cube of bread should turn golden in 30 seconds.

Fry the falafel in batches of 5 or 6, without crowding, for 3 to 4 minutes total, turning once, until deep golden brown and crisp on all sides. Lift with a slotted spoon and drain on a paper-towel-lined plate.

For the sauce: whisk the Greek yogurt, tahini, lemon juice, grated garlic, and salt in a bowl until smooth. Thin with 1 to 2 tablespoons water if needed to reach a pourable but coating consistency.

Serve four falafel per person, warm, with a generous spoon of tahini yogurt sauce alongside. Stuff into warm pita with sliced tomato, cucumber, pickled turnip, and shredded red cabbage for a full sandwich.