In a food processor or blender, process the chickpeas, lemon juice, and 1/4 cup of water until almost smooth. Transfer to a large bowl and add the shallot, cumin, red pepper flakes, 2/3 of the garlic, 1 teaspoon of the salt, 2 tablespoons of the parsley, and 1/2 cup of the bread crumbs and mix well. Roll into 16 balls (about 2 inches in diameter) and flatten slightly to form patties.
Place the remaining bread crumbs in a bowl or dish. Dip the falafel patties in the whisked eggs, then roll in the bread crumbs, coating evenly.
Prepare dip: In a medium bowl, combine the yogurt and pepper with the remaining garlic, salt, and parsley. Mix well. Cover and set aside.
Heat half the oil in a large skillet over medium heat. Place 8 of the chickpea patties in the pan and cook until golden brown, about 2 minutes per side. Drain on paper towels. Add the remaining oil, if necessary, and cook the remaining patties. Drain. Serve with the yogurt dip.
If You Don't Have... store-bought bread crumbs, make fresh ones in a food processor. One slice of bread yields about 1/2 cup crumbs.