Sift flour, baking powder and salt into medium bowl and set aside. In large bowl beat butter and sugar until lightened in color and fluffy, using an electric mixer on medium speed, about 2 minutes. Mix in egg yolks and vanilla. Add flour mixture, mixing on low speed just until flour is incorporated and soft, smooth dough forms. Divide dough into 2 pieces; form each into a log about 7 1/2 inches long and 1 1/2 inches in diameter. Wrap each in plastic wrap. Refrigerate about 1 hour until cold and firm, or overnight. Or freeze, wrapped securely, for up to 1 month. (Defrost in the refrigerator before slicing and baking.)
Position rack in middle of oven. Heat oven to 325 degrees F. Line two baking sheets with parchment paper. In small bowl, use fork to beat egg white until foamy, about 30 seconds. Use pastry brush to brush each log with egg white. Sprinkle the 1/3 cup sugar on strip of wax paper then roll each log back and forth in sugar to coat lightly. Use large sharp knife to cut each log into 1/4 -inch-thick rounds. Place 1 inch apart on prepared baking sheets. Press nut half into each cookie before baking, if desired. Bake one sheet at a time until cookie edges and bottoms are light brown, about 18 minutes. Cool 5 minutes on baking sheet, then transfer to wire rack to cool completely. Store in tightly covered container at room temperature up to 3 days.