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In a small bowl, mix together the lime juice and milk and set aside to curdle.
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In a large bowl, mix the butter and sugar.
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Add in the lime juice mixture and mix well.
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Add in the egg, flour, baking powder, and baking soda. Mix until the batter is a smooth consistency.
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Drop by teaspoonful onto a greased cookie sheet and bake for 8 minutes at 350 degrees or until the cookies begin to brown slightly.
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Remove from the oven and let the cookies cool before glazing.
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To make the glaze, mix the lime juice and powdered sugar together in a small bowl.
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Drizzle over the cooled cookies and enjoy!