For the falafel, in a medium bowl, cover the chickpeas and the baking soda with a few inches of water. Let sit overnight (the baking soda helps tenderize the beans). Or, to quick-soak them, place the chickpeas and baking soda in a medium bowl and top with 6 cups boiling water. Let stand at least 1 hour.
Drain the chickpeas well; transfer to a food processor. Add the remaining falafel ingredients. Pulse until the mixture looks like coarse sand. Transfer to a medium bowl, cover and refrigerate at least 1 hour. Form into 6 patties, each about 4 to 5 inches in diameter.
For the tahini sauce, in a blender or food processor, puree the lemon juice and garlic on high until smooth. Add the tahini and cumin and season with salt. Puree until the sauce is smooth and coats the back of a spoon, thinning with a little water if necessary.
In a large skillet, heat enough oil to coat in a thin layer over medium-high. Add the patties and cook until browned, 3 to 4 minutes. Flip; cook another 2 to 3 minutes. Top with cheese; tent the skillet loosely with foil and cook until the cheese melts, 1 to 2 minutes.
Pile a little lettuce, pickled veggies and tahini sauce on one side of each pita half. Top each with a patty and fold the pita over.