Cream butter in a large mixing bowl; gradually add 1 cup sugar, beating until light and fluffy. Add egg yolks, beating until well blended. Add enough flour to make a stiff dough. Roll to 1/4-inch thickness on a floured surface. Cut with a floured 2 3/4- inch doughnut cutter.
Place 2 inches apart on greased cookie sheets. Brush with lightly beaten egg whites. Combine remaining sugar, cinnamon, and pecans; sprinkle over cookies. Bake at 300° for 15 minutes or until lightly browned. Remove from cookie sheets, and cool on wire racks.