Coat a 9x13-inch metal baking pan with cooking spray and 1 tablespoon olive oil and place inside the oven. Preheat the oven to 375 degrees F (190 degrees C). C
Combine chickpeas, onion, cilantro, parsley, garlic, lemon zest, cumin, salt, red pepper flakes, and baking powder in a food processor. Pulse until minced but not yet pasty. Transfer to a bowl and stir in flour and egg until fully incorporated.
Remove baking pan from the oven. Drop golfball-sized portions of chickpea mixture onto the hot pan.
Bake in the preheated oven 15 to 20 minutes. Brush falafel with remaining olive oil and flip over. Continue baking until golden on both sides, 15 to 20 minutes more.
Meanwhile, combine yogurt, cucumber, lemon juice, and garlic in a bowl. Season with salt and cayenne pepper. Store in the refrigerator until ready to serve.