Preheat oven to 350. Line a cookie sheet with parchment paper.
Combine cookie ingredients in a bowl and mix with a wooden spoon. This dough comes together pretty easily. Divide into 16 pieces. Roll each into a ball and put on a cookie sheet lined with parchment paper. OR shape the dough into a log and slice 16 pieces.
Using the bottom of a measuring cup or drinking glass flatten the cookies to ¼ inch thick. They might stick to the bottom but just slide the dough off and put it back on the parchment.
Bake for 10-12 minutes until the edges are golden. (One reader said 8 minutes was enough so if your oven runs hot start checking after 8). Cool completely.
While the cookies are cooling mix the butter for the icing with an electric mixer. Slowly add the sugar and mix until smooth. Add the maple extract.
When the cookies are completely cooled flip half upside down and divide the icing between them. Top each with a second cookie. Refrigerate for at least an hour. Otherwise the icing with ooze out when you bite them.