For the cookies: In the bowl of a stand mixer fitted with a paddle attachment, combine the butter, cream cheese, and sugar. Beat on medium speed for 2 to 3 minutes, or until light and fluffy. Add the egg yolk and the vanilla, then mix on low until fully combined, scraping the bottom and sides of the bowl as needed.

In a medium bowl, whisk together the flour, cornstarch, baking powder, and salt. Gradually add the flour mixture to the butter mixture and mix on low speed until fully combined.

Remove the dough to a sheet of parchment paper and press the dough into a 5-inch square. Place another sheet of parchment paper over the square and use a rolling pin to roll the dough into a 14-by-10-inch rectangle. Chill the dough in the refrigerator until firm, 15 to 20 minutes.

For the filling: In a small bowl, stir together the brown sugar, flour, and cinnamon. Pour in the melted butter, stirring until the butter is evenly distributed and the mixture forms a paste.

Remove the dough from the refrigerator and remove the top piece of parchment paper. Using a small spatula, carefully dollop the filling all over the dough. Gently spread the filling into an even layer, reaching the edges of the dough as best you can.

Working slowly, carefully roll the dough from the long side into a tight log, removing the bottom layer of parchment as you roll. Carefully wrap the log in plastic wrap and chill in the refrigerator for at least 2 hours or overnight.

Preheat the oven to 350°F. Line 1 baking sheet with parchment paper.

Remove the dough from the refrigerator and, using a sharp knife, slice into ½-inch-thick rounds. Place the cookies 2 inches apart on the prepared baking sheet. Rewrap and refrigerate the remaining cookie dough until ready to slice and bake.

Bake until lightly browned, 10 to 12 minutes. Let the cookies cool on the baking sheet for about 5 minutes. Transfer them to a wire rack to cool completely. Repeat with the remaining cookies.

For the glaze: In a medium bowl, combine the powdered sugar, melted butter, and maple extract. Add the warm water, 1 teaspoon at a time, until the icing falls off the whisk in a fluid stream and the fallen ribbon of icing holds its shape for only a few seconds before sinking back into the bowl of icing.

Use a spoon to drizzle the glaze onto the cookies, or for a more even look, use a zip-top bag: Spoon the glaze into the bag and snip ⅛ inch off the end. Allow to set for 15 minutes.

Store the cookies in an airtight container at room temperature for up to 1 week.