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Empty the chickpeas into a bowl. Add the onion, parsley, cumin, coriander, garlic, black pepper, lemon juice, and cayenne. Mix gently with a fork. Do not pat down. This mixture should be loose and crumbly.
Put 2 inches / 5 cm of oil in a wok or other utensil for deep frying and set to a heat on a medium-low flame. You need a temperature of 350F to 375F (180C to 190C).
While the oil heats, form the first batch of patties. Using a very light touch, form patties that are about 2 1/4 inches / 5.5 cm in diameter, about 3/4 inch / 1.9 cm thick in the center and less so at the edges. Do not pat down or try to be too neat. The patties should just about hold together.
Put as many patties into the hot oil as the utensil will hold in a single layer. Fry about 4 minutes or until the patties a reddish brown on both sides. Turn at least once during the frying process. When the patties are done, remove them with a slotted spoon and drain on a paper towel. Do all of the patties this way.
Serve hot, with tahini dipping sauce. You may also tear open an end off a pita bread, stuff in two falafel and some shredded lettuce and sliced tomatoes, and then douse the stuffing with 2 T of tahini sauce to make a middle eastern sandwich. Don't forget to add the hot chilli pepper sauce or tabasco.
Makes about 18 patties.