These crispy, savory fritters are presented with classic tzatziki, a garlicky yogurt sauce.
In a medium saute pan, heat 3 tablespoons oil over medium heat. Add onion; cook, stirring, until soft and translucent, about 3 minutes. Add sesame seeds, cumin, and cayenne; cook, stirring, until the sesame seeds have begun to brown lightly and the spices are very fragrant, about 2 minutes; set aside.
In a food processor, combine chickpeas, lemon juice, egg white, salt, and 1 tablespoon oil. Pulse several times to form a semismooth paste. Transfer to a large bowl; stir in onion mixture. Fold in flour until just combined. Using your hands, form batter into 1 1/4-inch patties, each about 1/3 inch thick.
In a 12-inch saute pan, heat 2 tablespoons oil over medium-low heat. Cook half the patties, without flattening, until golden brown, about 3 minutes per side. Transfer patties to a paper-towel-lined plate, and season with salt. Repeat with remaining patties and tablespoon oil. Serve immediately with tzatziki.