Preheat your oven to 350°F (175°C) and line a baking sheet with parchment paper.
In a medium bowl, whisk together the flour, baking powder, and salt. Set aside.
In a large bowl, cream the softened butter and brown sugar together until light and fluffy, about 2-3 minutes.
Beat in the egg and vanilla extract until well combined.
Gradually add the dry ingredients to the wet mixture, mixing until just combined. If the dough is too dry, add milk a tablespoon at a time until it reaches a workable consistency.
Divide the dough in half and roll each half out on a lightly floured surface to about 1/4 inch thick. Cut out rectangles (about 3x4 inches) using a knife or cookie cutter.
Place half of the rectangles on the prepared baking sheet. Add a small dollop of your favorite jam or filling in the center of each rectangle.
Top each filled rectangle with another rectangle of dough. Press the edges together to seal, and use a fork to crimp the edges for a decorative touch.
Bake in the preheated oven for 12-15 minutes, or until the edges are lightly golden.
While the cookies are cooling, prepare the icing by mixing the powdered sugar with 1-2 tablespoons of milk until smooth. Adjust the consistency as needed.
Drizzle the icing over the cooled cookies and add sprinkles if desired. Allow the icing to set before serving.