Step 1

For the cookie dough: Cream together the butter, granulated sugar and brown sugar until light and fluffy, 3 to 4 minutes. Add the vanilla and egg and continue to mix until well incorporated, scraping down the sides of the bowl as needed. In a large bowl, stir together the flour, baking powder and nutmeg until well combined. With the mixer on low, add the flour mixture slowly until incorporated and the dough has come together. Cover and chill for 15 for 20 minutes.

Step 2

For the filling: Tip the dough out onto a floured surface. Roll out into a 16-by-8-inch rectangle about 1/4 inch thick. Pour over the melted butter and, using your hands, spread the butter evenly over the dough. Sprinkle over the cinnamon and then the granulated sugar. Starting with the long edge, carefully roll the dough tightly, just as you would with cinnamon rolls, and pinch the seam together when you reach the end. Cut the log in half. Wrap the logs in plastic wrap, put on a baking sheet and chill until firm, 45 minutes to 1 hour.

Step 3

Preheat the oven to 350 degrees F. Line 2 baking sheets with parchment paper and set aside.

Step 4

Unwrap the cookie dough and transfer to a cutting board. With a sharp knife, cut the logs into 1/2-inch pieces. Transfer the cookies to the prepared baking sheets and bake until set and the edges begin to brown slightly, 12 to 13 minutes. Transfer to a cooling rack to cool.

Step 5

For the glaze: Meanwhile, whisk together the confectioners' sugar, milk and melted butter in a large bowl until smooth. Add the maple extract and taste. Add more confectioners' sugar or butter as needed; the glaze should be thick but still pourable. Drizzle the glaze back and forth over the cookies and allow to set before serving, 10 to 12 minutes.