In a large mixing bowl, whisk together flour, baking powder, baking soda, and salt until well combined.

In another bowl, cream together butter, brown sugar, and granulated sugar until light and fluffy.

Add in egg and vanilla extract, mixing until fully incorporated.

Gradually blend the dry ingredients into the wet mixture until just combined.

Divide the dough into two equal portions and shape each into a flat disk.

Wrap each disk tightly in plastic wrap and refrigerate for at least 1 hour.

While the dough chills, mix together brown sugar, cornstarch, and cinnamon in a small bowl for the filling.

Preheat the oven to 350°F (175°C).

Roll out one disk of dough to about 1/4 inch thickness on a lightly floured surface.

Cut the rolled dough into rectangles, roughly 3x4 inches each, and place on a parchment-lined baking sheet.

Take half of the rectangles, add about 1 tablespoon of filling mixture in the center of each.

Top with another rectangle of dough, sealing edges by pressing down.

Brush tops lightly with milk for a golden finish.

Bake for 12-15 minutes or until edges are golden and tops are set.

Let cookies cool on the baking sheet for 5 minutes before transferring to a wire rack.

Whisk together powdered sugar and milk for the icing until smooth.

Drizzle the icing over cooled cookies and, if desired, add sprinkles.