1. In a large bowl beat butter with both sugars until creamy.
2. Add coconut, both zests, and vanilla. Mix well.
3. Add sifted flour in 2 or 3 parts, mixing until no dry spots remain.
4. On a piece of parchment or film paper put half the dough making a rough cylinder. With the aid of the paper, wrap it, smoothing the log. It doesn’t need to be perfect.
5. Close the ends and refrigerate until firm, 1 hour or up to 2 days.
6. Preheat oven to 325ºF 7 165ºC.
7. Line baking cookie sheets with parchment paper.
8. Cut logs into 1/4 inch rounds and place on the prepared sheets.
9. Bake for about 15 minutes, until they start to dry and turn golden.
10. Let cool on wire racks.

For the glaze:

1. Mix sugar and juice until smooth and creamy.
2. Glaze the top of the cooled shortbread cookies and finish with some zest before the glaze sets.
3. They keep for a few days or a week in sealed tins.