In a large bowl, cream butter and sugar until light and fluffy. Beat in egg yolks and corn syrup. Gradually beat in flour. Refrigerate, covered, 30 minutes or until firm enough to roll into balls.
For filling, in a small saucepan, combine icing sugar, butter and corn syrup. Bring to a boil over medium heat, stirring occasionally. Remove from heat; stir in pecans. Remove from pan; refrigerate 30 minutes or until cold.
Preheat oven to 375°F. Shape dough into 1″ balls; place 2″ apart on parchment lined baking sheets. In a small bowl, whisk egg whites; brush over tops. Bake 5 minutes. Remove from oven. Gently press an indentation in center of each cookie with the end of a wooden spoon handle. Fill each with 1/2 teaspoon pecan mixture. Bake 4-5 minutes longer or until edges are light brown.
Cool on pans 5 minutes. Remove to wire racks to cool. Yield: 4-1/2 dozen.