Heat the oven to 400°F (200°C). Brush a sheet pan with 2 tablespoons of the oil.
Pat the soaked chickpeas dry. Put them in a food processor with the onion, garlic, herbs, cumin, coriander and salt. Pulse, scraping down the sides, until finely chopped and the mixture holds together when pressed, like coarse sand. Do not purée it.
Pulse in the baking powder and flour. Shape into 16 small patties about 1/2 inch thick and place them on the pan. Brush the tops with the remaining oil.
Bake for 12 minutes, flip carefully, and bake for 10–13 minutes more, until golden and crisp on both sides.
Meanwhile, whisk the tahini, lemon juice and a pinch of salt. It will seize up at first; whisk in cold water a spoonful at a time until smooth and pourable.
Warm the flatbreads, then fill each with lettuce, tomato, cucumber, 4 falafel and a drizzle of tahini sauce. Roll up and serve.