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To make the dough: In the bowl of an electric mixer, beat together the butter, salt, sugars, and maple flavor.
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Add the flour and mix just until the dough comes together. Wrap the dough in plastic and chill for 30 minutes. The dough can chill longer than 30 minutes, but if it does, allow about 15 minutes for it to warm a bit and soften before rolling it out.
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Preheat the oven to 300°F. Lightly grease a baking sheet, or line it with parchment.
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On a lightly floured surface, roll the dough about 1/8" thick.
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Use a cutter to cut the dough into shapes — leaves, stars, hearts, circles, your choice. To make the thicker stamped cookies pictured above, see "tips," below. Place the cookies on the prepared baking sheet.
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Bake the cookies for 20 to 25 minutes, until they're beginning to brown a bit. Remove them from the oven, and cool right on the pan.
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To make the filling: Mix together all of the filling ingredients except the milk, stirring until smooth. If the filling isn't spreadable, add a bit of the milk to soften its texture.
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To assemble the cookies: Spread the bottom of half the cookies with filling; if you have a scale, about 14g (1/2 ounce) is a good amount for each. Top with the remaining cookies.
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Store cookies, well wrapped, at room temperature for several days. Freeze for longer storage.