In a large mixing bowl, cream together softened unsalted butter with brown sugar and granulated sugar until light and fluffy, about 3-5 minutes. Beat in the eggs and vanilla extract until well combined. Gradually mix in the flour, baking powder, baking soda, and salt until just blended.

In a separate bowl, combine brown sugar with cinnamon. Slowly add in milk, mixing until the filling reaches a smooth, spreadable consistency. Set the filling aside.

Divide the cookie dough into two equal portions. Roll one half out to about ¼ inch thick, and cut into rectangles, about 3x4 inches.

Place a generous teaspoon of the filling in the center of one rectangle of dough. Cover with a second rectangle, pressing edges to seal. Repeat until all dough and filling are used.

Preheat oven to 350°F (175°C). Line baking sheet with parchment paper, arrange cookies leaving space for spreading. Bake for 12-15 minutes, or until golden brown.

Let cookies cool on the baking sheet for about 5 minutes, then transfer to a wire rack. Prepare icing by whisking together powdered sugar and milk. Drizzle over cooled cookies and add sprinkles if desired.