Drain and rinse the overnight-soaked chickpeas, ensuring they are completely dry before processing to prevent mushy falafel. Add the chickpeas, parsley, cilantro, onion, garlic, cumin, coriander, salt, and black pepper to a large food processor.

Pulse the mixture until it resembles coarse sand, scraping down the sides of the bowl as needed so everything is evenly minced. Transfer the falafel mixture to a bowl, stir in the baking soda, and let it rest in the refrigerator for 15 minutes to firm up.

While the mixture rests, prepare the tahini sauce by whisking together the tahini, fresh lemon juice, and a pinch of salt in a small bowl. Gradually whisk in the warm water, one tablespoon at a time, until the sauce reaches a smooth, pourable consistency.

Heat about 2 inches of vegetable oil in a deep skillet or heavy pot over medium-high heat until a thermometer registers 350 degrees F. Use your hands or a small cookie scoop to form the chilled falafel mixture into 1-inch balls or slightly flattened patties.

Carefully drop the falafel into the hot oil in batches, being careful not to overcrowd the pan and lower the oil temperature. Fry for 3 to 4 minutes, turning occasionally, until they are deeply golden brown and crispy all over.

Remove the fried falafel with a slotted spoon and transfer them to a paper towel-lined plate to drain any excess oil. Warm the pita halves in the microwave or oven for about 15 seconds so they are soft and easy to open into pockets.

To assemble, stuff each warm pita pocket with 3 to 4 crispy falafels, diced cucumber, and diced tomatoes. Drizzle generously with the prepared tahini sauce and serve immediately alongside extra napkins for a messy but delicious meal.