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Preheat oven to 350 degrees and line 2 baking sheets with parchment paper or a silpat.
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In the bowl of your mixer, beat butter, sugar, and coconut extract until light and fluffy.
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Add lime zest and lime juice and beat until combined.
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Add eggs, one at a time, mixing throughly after 1st addition.
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In a separate bowl, combine flour, alt, baking powder and soda.
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With your mixer running on low, gradually add dry mix to wet mix, mixing until just combined.
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In a small bowl add powdered sugar.
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Roll a heaping tablespoon of dough and place it in the bowl of powder sugar and coat completely.
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Place on cookie sheet and repeat with remaining dough placing each ball about 2 inches apart.
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Bake at 350 degrees for 9-11 minutes. Cool completely.
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To make the frosting beat the cream cheese, powdered sugar, lime juice and lime zest on medium high speed until smooth.
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Stir in toasted coconut.
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Top cooled cookie with frosting and sandwich with another cookies.