In a small bowl, cream the butter, sugar and vanilla until light and fluffy. Gradually add flour and mix well. On a lightly floured surface, roll out half of the dough to 1/8-in. thickness. Cut with a floured 2-in. round cookie cutter. Repeat with remaining dough, using a floured 2-in. doughnut cutter so the center is cut out of each cookie.
Place 1 in. apart on lightly greased baking sheets. Brush egg white over cookies with cutout centers; sprinkle with coconut. Bake at 350° for 8-10 minutes. Remove to wire racks to cool.
For filling, in a large saucepan, combine sugar and cornstarch; stir in water until smooth. Cook and stir over medium-high heat until thickened and bubbly. Reduce heat to low; cook and stir for 2 minutes longer. Remove from the heat. Stir a small amount of hot filling into egg yolk; return all to the pan, stirring constantly. Bring to a gentle boil; cook and stir for 2 minutes. Remove from the heat; gently stir in butter and lemon juice. Cool to room temperature without stirring.
Spread a teaspoonful of filling on the bottom of each solid cookie; place coconut topped cookie over lemon filling. Store in the refrigerator. Yield: 1-1/2 dozen.