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Preheat oven to 350 degrees. Line cookie sheets with parchment paper.
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In a small bowl, stir together flour, baking soda, baking powder and salt. Set aside.
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Using a mixer, beat together the butter and sugar until smooth and very fluffy.
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Beat in egg, vanilla extract, lime juice and lime zest.
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Gradually blend in the dry ingredients and toasted coconut.
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Roll rounded teaspoonfuls of dough into balls, and roll in sugar. Place on lined cookie sheets about 1 1/2 inches apart. Press down lightly with the bottom of a drinking glass to flatten the balls slightly.
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Bake 10 minutes in the preheated oven, or until lightly browned at the bottom edges. (Depending on their size and the pans you are using, these could take longer. Darker pans tend to bake faster. Aluminum bakeware may take about 12-13 minutes. They can be quite pale on top and still be baked, just check that the bottoms are golden brown. As always I recommend baking just 2 or 3 on the sheet first as a test, to get the right time for your oven and bakeware.)
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Let stand on cookie sheet two minutes before removing to cool on wire racks.