Preheat the oven to 325° F and line 2 large baking sheets with parchment paper.
In the bowl of a stand mixer, fitted with the paddle attachment, cream the butter and sugar together until light and fluffy, for about 3-4 minutes. Add the coconut, flour, cornstarch, salt and lemon zest and continue mixing just until dough begins to come together. Dump dough onto the counter and finish mixing by hand.
Divide dough in half and roll out each piece of the dough, between 2 sheets of parchment paper to a ¼ inch thick thickness. Chill dough for about 30 minutes.
After chilling, peel off top parchment sheet and gently lay it back in place. Flip the dough over; peel off and discard second parchment layer.
Cut the dough, using cookie cutters of your choice. I used a few different sizes of snowflake cutters, ranging from. 5 inches to 2 inches. Transfer shapes to prepared baking sheets, using a wide metal spatula, spacing them 1 inch apart. Chill snowflakes in freezer for about 10 minutes to firm them up again. Set scraps aside.
While cookies are chilling, place sugar and coconut for the topping, in a spice grinder or food processor, and pulse a few times to coarsely grind.
Sprinkle cookies liberally with sugar-coconut topping and bake for 6 minutes. Switch position of trays and bake for a further 7-8 minutes, until the cookies are lightly golden brown. Carefully lift one of the cookies with a spatula to check the bottom of the cookie. It should be lightly browned. Bake for a few more minutes, if it is still pale.
These are fragile cookies so you must let them cool completely on the baking sheet, set on a rack. Store in an airtight container. They will keep for about a week at room temperature, or can be frozen for 2 months.
Gather the scraps; repeat rolling, cutting and baking.