Falafel and Cucumber Sauce

Method

1. Soak the dried chickpeas in cold water to cover by 3 inches (7.6 cm) for at least 12 hours, until they have tripled in size and a chickpea splits cleanly when pinched. Do not cook them and do not substitute canned chickpeas; boiled chickpeas make a paste that falls apart in the oil. Drain and dry them well.
2. Grate the English cucumber, squeeze it dry in a towel, and stir it into the whole milk Greek yogurt with the lemon juice, fresh mint, and 1/2 teaspoon of the kosher salt. Refrigerate the sauce while you make the falafel.
3. Grind the drained raw chickpeas with the yellow onion, garlic, fresh parsley, fresh cilantro, ground cumin, ground coriander, cayenne pepper, and the remaining 2 teaspoons kosher salt in a food processor, in two batches, pulsing to the texture of coarse wet sand that holds when squeezed. Do not puree it smooth.
4. Refrigerate the mixture for 1 hour, then stir in the baking soda and the sesame seeds right before frying. Baking soda added early loses its lift; added now it gives the interior its fluff.
5. Shape into 1 1/2-inch (3.8 cm) balls or thick discs, pressing firmly. Test one first: if it disintegrates in the oil, pulse the remaining mixture a few more times to bind it.
6. Heat the vegetable oil to 350 degrees F (177 degrees C) in a deep pot and fry the falafel in batches of six for 3 to 4 minutes, turning once, until deep mahogany and crisp. Drain on a rack, not paper towels.
7. Serve hot in the warmed pita breads with the cucumber sauce; falafel loses its texture within about ten minutes of leaving the oil.