Chicken Schnitzel with Frisée-Apple Salad

Place large piece of plastic wrap on work surface. Unfold 1 chicken thigh near 1 end of plastic. Fold other end of plastic over chicken to cover completely. Using mallet, pound chicken to 1/4- to 1/3-inch thickness. Set cutlet aside in plastic sheet. Repeat with remaining chicken thighs and 5 more sheets of plastic wrap. DO AHEAD: Cutlets can be made up to 1 day ahead. Refrigerate wrapped in plastic. Place large scoop of flour in shallow dish (such as pie dish). Beat eggs and parsley in another shallow dish to blend. Place 2 cups breadcrumbs in third shallow dish. Unwrap 1 chicken cutlet and sprinkle all over with salt and pepper. Coat cutlet completely with flour, then egg mixture, then breadcrumbs. Transfer cutlet to rimmed baking sheet. Repeat with remaining chicken cutlets, adding more flour and breadcrumbs as needed. Divide half of butter and half of oil between 2 large skillets; melt butter with oil over medium-high heat. Add 3 cutlets to each skillet. Cook until coating is golden brown and crisp on bottom, about 3 minutes. Using spatula, transfer chicken to sheet of foil. Divide remaining butter and remaining oil between skillets; swirl to melt butter. Return chicken, browned side up, to skillets. Sauté until bottoms are browned and chicken is cooked through, about 3 minutes longer. Transfer chicken to plates. Serve with Frisée-Apple Salad .