Heat oven to 350 degrees F and arrange a rack in the middle.
Combine the flour, zest, and salt in a large bowl and whisk until evenly combined.
Using a stand mixer fitted with a paddle attachment beat together butter and sugars over high speed until light and airy, about 2 minutes. Add the sugars and beat until fluffy and the mixture looks like wet sand, about 2 more minutes. Add the egg and vanilla and mix until just combined.
Reduce the speed to medium and add the flour mixture and coconut and beat until just evenly combined. Lay 2 large pieces of plastic wrap on a clean work surface and put half of the dough along the center of each piece. Shape the dough into 2 logs measuring about 1 1/2-inches in diameter and 10-inches long. Roll logs up in the plastic and secure tightly. Refrigerate the logs for 1 hour or up to several weeks.
Cut the logs into 1/2-inch slices. Roll the cookies in sugar to coat and shake off excess. Arrange on a baking sheet, leaving 1/2-inch between the cookies. Bake until set and golden on the edges, about 15 to 18 minutes. Remove to cooling racks to cool completely.
When cookies are cool, melt the chocolate in a small pan over medium-low heat until smooth. Dip half of each cookie into the chocolate, scrape off excess, and set on a cooling rack. Refrigerate for at least 15 minutes to set up before serving.