In a large bowl, cream together the softened butter and granulated sugar using an electric mixer until light and fluffy.

Beat in the egg and vanilla extract until well combined.

In a separate medium bowl, whisk together the all-purpose flour, baking powder, and salt.

Gradually add the dry ingredients to the wet ingredients, mixing on low speed until just combined and a soft dough forms. Be careful not to overmix.

Divide the dough in half. Flatten each half into a disk, wrap tightly in plastic wrap, and refrigerate for at least 30 minutes (or up to 2 hours) to firm up. This makes the dough easier to handle.

While the dough chills, combine the packed light brown sugar, flour, and ground cinnamon in a small bowl.

Pour in the melted butter and milk (or water) and mix thoroughly with a fork until a thick, spreadable paste forms. Set aside.

Preheat your oven to 375°F (190°C). Line two large baking sheets with parchment paper.

On a lightly floured surface or between two sheets of parchment paper, roll out one disk of chilled dough to an even thickness of about 1/8-inch. Try to keep a rectangular shape.

Using a pastry wheel or a sharp knife, cut the dough into rectangles approximately 2x3 inches. You should yield about 12-15 rectangles from one dough disk.

Place half of the cut rectangles (these will be the bottom pieces) onto the prepared baking sheets, ensuring there's some space between them.

Spoon about 1 teaspoon of the brown sugar filling onto the center of each dough rectangle, leaving a small border (about 1/4 inch) around all edges.

Carefully top each filled rectangle with another plain dough rectangle. Gently press the edges together to seal.

Use the tines of a fork to crimp all around the edges of each cookie, firmly sealing the filling inside and creating the classic pop tart look.

Repeat steps 9-14 with the second disk of dough and the remaining filling.

Bake the cookies for 12-15 minutes, or until the edges are lightly golden brown and the tops are set. Baking time may vary depending on your oven.

Remove the baking sheets from the oven and let the cookies cool on the sheets for 5 minutes before carefully transferring them to a wire rack to cool completely. They are delicate when warm.

In a small bowl, whisk together the powdered sugar, 2 tablespoons of milk (or water), and vanilla extract until completely smooth. Add more milk, 1/2 teaspoon at a time, if needed, until you achieve a thick but pourable consistency for the glaze.

Once the cookies are completely cool to the touch, drizzle or spread the prepared glaze evenly over the tops of each cookie.

Allow the glaze to set for about 15-20 minutes at room temperature before serving to prevent smudging.