Pulse half each of the parsley and onion, the cumin, 1/2 teaspoon salt and a few grinds of pepper in a mini food processor to make a paste. Put the chickpeas in a large bowl and roughly mash with a potato masher, leaving some whole. Add the parsley mixture, egg and 1/2 cup panko; stir to combine. Refrigerate 10 minutes.
Meanwhile, combine the tomatoes, the remaining parsley and onion and 1/2 teaspoon salt in a medium bowl; set aside. Whisk the hummus and yogurt in another bowl to make a dressing.
Put the remaining 1 cup panko on a baking sheet. Scoop tablespoonfuls of the chickpea mixture and roll in the panko to coat and form a ball. Heat 1 inch vegetable oil in a large high-sided skillet over medium-high heat. Fry the falafel, turning often, until golden, about 6 minutes. Remove to a paper towel-lined plate to drain.
Toss the lettuce with half of the hummus dressing in a large bowl. Top with the tomato mixture and falafel. Serve with the remaining hummus dressing.