Place coconut and sugar in a food processor; cover and process until coconut is coarsely chopped. In a large bowl, cut butter into flour until crumbly. Stir in coconut mixture. Stir in eggs and vanilla., On a lightly floured surface, roll out dough to 1/8-in. thickness. Cut with a 2-1/2-in. heart-shaped cookie cutter dipped in flour. Using a 1-in. heart-shaped cookie cutter, cut out the center of half of the cookies. Reroll small cutouts if desired. , Place solid and cutout cookies 1 in. apart on greased baking sheets. Bake at 375° for 7-9 minutes or until edges are lightly browned. Remove to wire racks., In a small bowl, combine the confectioners' sugar, water and vanilla; brush over warm cookies with cutout centers. Immediately sprinkle with coarse white sugar if desired. Spread 1/2 teaspoon of jam over the bottom of each solid cookie; place cookies with cutout centers over jam.