In a small bowl, mix the cucumber, yogurt, garlic, dill, oil and salt together. Refrigerate the sauce until serving so all the flavors have time to meld. Editor's Tip: Two cloves of garlic can pack a punch. Make the sauce first to allow that garlic some time to mellow out in the fridge.
In a shallow bowl, whisk together the flour, salt, pepper and baking powder. In another bowl, whisk together the egg and milk. Set aside while you pound the chicken. Using a meat mallet, pound the chicken breasts to ½-inch thickness. Working with one chicken piece at a time, dip the chicken in the flour mixture to coat both sides, shaking off any excess flour. Dip in the egg mixture, then back in the flour mixture. Editor's Tip: Lay the breaded chicken on a baking sheet—even better, on a rack fitted on the baking sheet—while you repeat with the remaining chicken breasts.
In a large skillet, heat the oil over medium heat. Cook the breaded chicken until golden brown on both sides and any juices run clear, five to seven minutes per side. Sprinkle the tops with feta cheese. Serve with tzatziki sauce and, if desired, additional fresh dill and lemon wedges. Editor's Tip: You can let the chicken rest for a few minutes before you top it and serve it. This will let the juices redistribute in the meat so that it's nice and moist when you cut into it.
