Cover dried chickpeas with the soaking water and refrigerate for 12 to 18 hours. Drain thoroughly and spread on a clean towel to dry; do not cook them before mixing.

Pulse chickpeas, onion, garlic, parsley, cilantro, cumin, coriander and 3/4 teaspoon salt in a food processor until finely chopped and cohesive when squeezed, scraping down several times without turning into a smooth paste.

Mix in chickpea flour and baking powder. Refrigerate for 30 minutes, then shape into 16 equal balls, about 1 1/2 inches across, pressing firmly.

Heat frying oil to 350°F in a heavy deep pot that is no more than half full. Fry four falafel at a time for 4 to 5 minutes, turning gently, until deeply golden and cooked through; split one to check that the center is hot and tender rather than raw and pasty.

Keep cooked falafel on a rack in a 200°F oven while finishing four total batches. Stir tahini, lemon juice, 3 tablespoons cold water and remaining salt until smooth, adding the extra tablespoon water only if needed for a drizzling consistency.

Wrap pitas in foil and warm in the oven for 5 minutes. Cut each across the middle to make eight half-pockets and open carefully.

Put two hot falafel balls in each half-pocket with tomato, cucumber and tahini sauce. Serve two filled half-pitas per person immediately.