Put the dried chickpeas in a large bowl and add cool water to cover by 2 inches. Soak the beans in the refrigerator for at least 18 hours or up to 24; the chickpeas will swell to triple their original size. Drain and rinse thoroughly.
Put the soaked chickpeas in a food processor and pulse to coarsely grind, not until smooth but with no whole chickpeas remaining either. Add the baking powder, onion, garlic, spices, and herbs; process until the mixture is pureed; scraping down the sides of the bowl as needed. Taste and season with salt and pepper. Transfer to a bowl and refrigerate while heating the oil, this should take about 15 minutes.
Pour 3-inches of the oil in a deep fryer or deep heavy pot and heat to 375 degrees F.
Roll the falafel mixture into ping-pong size balls. (Alternatively, use an ice cream scoop.) Carefully slip a few at a time into the hot oil, making sure they don't stick to the bottom. Fry until the chickpea fritters are a crusty dark brown on all sides, turning as needed, about 5 minutes per batch. Remove the falafels with a slotted spoon and drain on a platter lined with paper towels.
Open the pita bread halves to make pockets (don't split all the way) and put 4 fried falafels into each. Drizzle with the tahini sauce and layer with lettuce, tomatoes, and cucumbers. Serve immediately.
Combine all the ingredients in a blender, process on high speed to make a smooth and creamy sauce. Adjust seasoning, to taste, and serve with falafels or as a salad dressing.