Preheat the oven to 350 degrees. Line a baking sheet with a Silpat mat.
Combine the flours, baking soda, baking powder, and salt in a bowl. Using a mixer, beat together the butter and sugar until fluffy.
Slice the vanilla bean down the center lengthwise without cutting all the way through the underside.
Take the back of your knife and scrape out all the seeds from inside the bean. Place the seeds into the sugar mixture.
Add the egg, lime juice, and lime zest to the mixture, then beat with a hand mixer or in a stand mixer until well combined.
Gradually mix in the dry mixture and the coconut into the sugar mixture until combined. Don't overmix.
Roll the dough into small balls, then place the balls in a bowl of white sugar (about ½ cup). Roll the balls in the sugar, then put them on the lined baking sheet about 1½ inches apart.
Bake for 8-10 minutes or until lightly browned.
Remove from the oven and let cool on a wire cooling rack. Enjoy.