Season chicken with salt and pepper. Place in a large resealable plastic bag with 1/4 cup olive oil, thyme and garlic; seal bag and refrigerate for several hours or overnight. Remove chicken from marinade and place between 2 pieces of plastic wrap; pound with a meat mallet until 1/2-inch thick.
Place 1/2 cup flour in a shallow dish. Mix the remaining flour, panko breadcrumbs and walnuts in a second shallow dish. Beat egg whites with milk in a third dish.
Dip each piece of chicken in flour, then egg mixture, then in the breadcrumb mixture.
Let rest for 10 minutes in the refrigerator until chicken is completely chilled and breading has set.
Heat remaining 1/2 cup olive oil in a large skillet until very hot.
Pan fry chicken for about 2 minutes on each side or until golden brown.