In a mixing bowl, cream butter and sugar. Beat in egg and vanilla. Gradually add flour. Divide dough in half; wrap each portion in plastic wrap. Refrigerate for 2 hours or until easy to handle; unwrap. On a lightly floured surface, roll out each portion of dough to 1/8-in. thickness. Cut with a 2-1/2-in. scalloped cookie cutter dipped in flour. Cut a 1-in. hole in the center of half of the cookies with a bottle cap. Place 2 in. apart on ungreased baking sheets. Bake at 375 degrees F for 8-10 minutes or until lightly browned. Remove to wire racks to cool.
In a saucepan, heat butter over medium heat until golden brown. Remove from the heat; gradually add sugar, vanilla and enough water to achieve a spreading consistency. Spread on the bottom of the solid cookies; place cookies with cutout centers over filling so the scallop edges alternate. Place 1/2 teaspoon preserves in center of each.