Cream butter in a medium mixing bowl; gradually add powdered sugar, beating until light and fluffy. Add egg yolks and water, beating until well blended.
Combine flour and salt in a small mixing bowl. Add to creamed mixture, beating well. Stir in vanilla.
Drop dough by teaspoonfuls 2 inches apart onto greased cookie sheets. Place a pecan half in center of each cookie; press down slightly. Bake at 375° for 8 minutes or until lightly browned. Remove from cookie sheets, and cool on wire racks.