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Heat oven to 350F and line two baking sheets with parchment paper or a reusable liner.
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In the bowl of a stand mixer, beat eggs and sugar together until frothy.
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Mix in oil, lemon zest, and vanilla.
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In a separate bowl mix the flour and baking powder together and add it while stirring into the wet ingredients - the dough should be firm and easy to manipulate.
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Transfer the dough onto a floured surface and shape into a ball and cut it into quarters.
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Take a quarter and cut into 12 equal pieces, roll each piece into a large snake and then shape the cookies into a twist. Do this until you have about 4 dozen cookies.
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Bake cookies one baking sheet at a time until they are slightly golden around the edges, about 10 to 15 minutes depending on your oven. Let cool on baking sheet.
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Once completely cooled, ice them by mixing together lemon juice and icing sugar and dunking the top of the cookie into the icing and placing them back on the cookie sheet, adding the sprinkles on top.
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Allow the icing to harden before storing.