In a large bowl, cream together the softened butter and granulated sugar until light and fluffy using a stand mixer or hand mixer. Beat in the egg and vanilla extract until well combined.

In a separate 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. Do not overmix.

Shape the dough into a disc, wrap it in plastic wrap, and refrigerate for at least 30 minutes to firm up.

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

Melt 1/4 cup of butter in a small saucepan. Stir in the brown sugar until well combined and slightly bubbly. Remove from heat.

Pour about 1/2 teaspoon of the butter-brown sugar mixture onto the parchment paper for each cookie, spreading it slightly into a small circle (about 1.5 inches in diameter). You will need 24 such circles.

Take the well-drained pineapple slices and cut them into quarters or small chunks that will fit neatly onto the brown sugar circles. Place one piece of pineapple on top of each brown sugar circle. Place a halved maraschino cherry, cut-side down, in the center of each pineapple piece.

On a lightly floured surface, roll out the chilled cookie dough to about 1/4-inch thickness. Use a 2.5-inch round cookie cutter to cut out 24 cookie circles.

Carefully place one cookie dough circle on top of each pineapple and cherry arrangement, gently pressing down to seal the edges around the pineapple. Ensure the pineapple and cherry are completely covered by the dough.

Bake for 10-12 minutes, or until the edges of the cookies are lightly golden. The cookies will puff up slightly.

Immediately upon removing from the oven, let the cookies cool on the baking sheet for 2-3 minutes. Then, working carefully and quickly, invert each cookie onto a wire rack. The pineapple topping should now be facing up, caramelized and slightly glossy. If any pineapple sticks, gently coax it off the parchment and place it back on the cookie. Allow the cookies to cool completely on the wire rack.

While the cookies cool, prepare the glaze. In a small bowl, whisk together the powdered sugar and 2 tablespoons of the reserved pineapple juice until smooth. If the glaze is too thick, add more juice, 1/2 teaspoon at a time, until it reaches a drizzling consistency.

Once the cookies are completely cool, drizzle the glaze over the pineapple topping of each cookie.