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1
Place the butter in a mixing bowl, and beat with an electric mixer on high speed until smooth and creamy, about 2 minutes. Gradually beat in 2/3 cup of confectioners' sugar, then add almond extract, eggs, and salt, and beat until the mixture is fluffy and well combined, about 3 more minutes. Reduce mixer speed to medium, and gradually beat in flour until the dough is smooth, about 1 minute. Gently stir in the maraschino cherries.
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2
Form the dough into 2 logs about 1 inch in diameter, roll each log in plastic wrap or waxed paper, and refrigerate until thoroughly chilled, at least 2 hours.
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3
Preheat oven to 350 degrees F (175 degrees C). Line several baking sheets with parchment paper.
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4
Cut each dough log into about 25 slices about 1/2-inch thick, and place the cookies on the prepared baking sheets, leaving about 1/2 inch of space between each cookie.
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5
Bake in the preheated oven until the cookies are set but not browned, 12 to 14 minutes. Remove to cooling racks to cool to room temperature, about 15 minutes.
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6
To make icing, beat egg whites with lemon juice until frothy, about 1 minute, then beat in vanilla extract and confectioners' sugar, a cupful at a time, until the icing is smooth and spreadable. Spread about 1 teaspoon of icing on each cooled cookie, and let the icing harden before stacking.
