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For the cookies: In a medium bowl, whisk together the flour, baking powder and salt. In a separate large bowl using an electric mixer, beat together the butter, granulated sugar and brown sugar, mixing until pale yellow and fluffy, 3 minutes. Add in the maple extract and eggs and mix well. Slowly incorporate the dry ingredients into the wet ingredients and mix well.
Transfer the dough to a floured work surface, divide into two disks, wrap in plastic and chill in the refrigerator for about an hour.
Preheat the oven to 350 degrees F. Line two baking sheets with parchment paper.
Working with one disk at a time, roll out the dough to 1/4-inch thickness. Cut out present shapes with the cookie cutter and place the cookies 2 inches apart on the prepared baking sheets. Re-roll the scraps to get as many cookies as possible, returning the dough to the refrigerator to chill if necessary.
Bake just until the edges start to brown, 10 to 12 minutes. (Bake one sheet at a time for even cooking and browning.) Transfer the cookies to a wire rack and let cool.
For the penuche icing: In a small saucepan , combine the brown sugar and butter and set over medium-high heat. Bring to a boil and cook until slightly thickened, about 1 minute. Let cool for 10 minutes. Slowly add the milk and whisk until smooth. Slowly whisk in the confectioners' sugar until the frosting reaches the desired consistency.