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In the bowl of a stand mixer, cream together the butter and powdered sugar.
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Add the vanilla and lemon juice and mix until just combined.
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With the mixer on low, add in the flour, salt, 2 teaspoons of the lemon zest and rosemary and allow to mix until a dough forms. Do not over mix.
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Using your hands, roll the dough into a log shaped, approximately 2.5 in diameter and cover with plastic wrap.
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Chill the dough for at least an hour.
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Preheat the oven to 350 degrees. Line a cookie sheet with parchment paper.
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With a serrated knife, gently slice the chilled dough into 1/4 inch thick cookie rounds.
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Place the rounds on your prepared cookie sheet, allowing a half inch between cookies.
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Bake at 350 degrees for approximately 12 minutes, or until the edges are just golden brown.
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While the cookies are baking, prepare the glaze by gently whisking together the powdered sugar and lemon juice.
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Remove the cookies from the oven and allow them to cool.
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When mostly cool, top the cookies with a small amount of the glaze and sprinkle each cookie with the remaining lemon zest and a small amount of turbinado sugar.
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Keep in an airtight container for up to a week or freeze.