Drain the soaked chickpeas well and pat dry. Do not cook them - raw, soaked chickpeas are what give falafel its texture.
In a food processor, pulse the chickpeas, onion, garlic, parsley, and cilantro until finely chopped but not pureed to a paste - it should still have some texture.
Transfer to a bowl and stir in the cumin, coriander, baking powder, salt, and pepper. Add flour a tablespoon at a time if the mixture feels too wet to hold together.
Cover and refrigerate for at least 30 minutes to firm up.
Heat about 2 inches of oil in a deep pot to 350°F (175°C). Scoop the mixture into 1.5-inch balls and fry in batches for 3-4 minutes, until deeply golden brown and crisp on the outside.
Remove with a slotted spoon and drain on paper towels.
For the tahini sauce, whisk together the tahini, lemon juice, garlic, and enough water to reach a pourable consistency. Season with salt to taste.
Serve the falafel warm with tahini sauce, warm pita, a fresh tomato-cucumber salad, and lemon wedges.