1Pulse the drained chickpeas, chopped onion, parsley, cilantro, and garlic in a food processor until the mixture is coarse and combined (should look like wet sand, not a paste).
2Add cumin, coriander, baking powder, salt, black pepper, and flour. Pulse until just mixed. Chill the mixture for 15 minutes if you have time.
3Heat the oil in a large pot to 350°F. Line a plate with paper towels.
4While oil heats, whisk together yogurt and lemon juice in a small bowl. Season with salt and pepper.
5Form the falafel mixture into small golf-ball-sized rounds. Flatten slightly with your palm.
6Working in batches, carefully lower falafel into the hot oil. Fry for 2 to 3 minutes per side until deep golden brown. Transfer to paper towels.
7Warm the pitas in a skillet or over a flame for 10 seconds per side.
8Lay out each pita, spread yogurt sauce inside, then layer cucumber, tomato, red onion, and 3 to 4 hot falafel. Serve immediately.
9Let the oil cool completely in the pot before you move it, which takes an hour or more. Strain it through a fine sieve into a jar and it is good for two or three more fries; otherwise seal it and discard it. Never pour frying oil down the drain — it hardens in the pipe.