Preheat the oven to 350°F (175°C) and lightly coat two 12-cup muffin pans with nonstick spray or line with paper cups.
For the topping, stir the melted butter together with the brown sugar in a small bowl until well blended. Spoon 1 teaspoon of the sugar-butter mixture into the base of each muffin cup.
Place a halved pineapple ring over the sugar in each cup, then nestle a maraschino cherry in the center of the ring.
To prepare the dough, beat the softened butter and granulated sugar in a large mixing bowl until the texture is airy and light, about 2 minutes.
Incorporate the egg, vanilla, and pineapple juice into the creamed mixture, mixing just until combined.
In a separate bowl, whisk together the flour, baking powder, baking soda, and salt until evenly distributed.
Gradually incorporate the dry mixture into the wet ingredients, stirring until a cohesive and soft dough develops.
Form the dough into balls roughly 1 1/2 inches in diameter. Lightly press each ball into a disc and set it atop the pineapple in the muffin tins, applying gentle pressure.
Bake for 11 to 13 minutes, or until the edges of the cookies begin to turn golden.
Once removed from the oven, allow the cookies to cool in the tins for 5 minutes. Then, carefully invert the pans over a wire rack or baking sheet so the fruit layer is on top.
Let the cookies cool completely before serving to ensure the topping is set and stable.