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Make the dough: in a big bowl, beat together the butter, sugars, cream of tartar, salt, eggs, baking soda, and maple extract until fluffy.
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Add the flour; beat until blended; refrigerate dough for about 30 minutes, to stiffen it and make it easier to shape.
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Make the coating: combine the sugars in a shallow bowl or pie plate, or in a large plastic bag.
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Drop the dough by the rounded tablespoonful into the coating, gently shake the pan to coat the balls, then roll them in your hands until they are smooth and round.
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Place the balls on baking sheet that has been sprayed with cooking spray, about 1 ½ inches apart.
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Bake in a 400° oven for 10-12 minutes, until they are very light golden brown; remove them from the oven and after 5 minutes, transfer them to a rack to cool.
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Make the glaze: in a bowl, stir together the powdered sugar, maple syrup, cream, and extract to make a spreadable frosting.
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Spread a thin layer over the cookies; let the glaze dry for several hours before packaging the cookies for storage.