Preheat your oven to 350 degrees F (175 degrees C).
In a large mixing bowl, cream together the room temperature butter and granulated sugar until light and fluffy.
Add the eggs one at a time, mixing well after each. Stir in the vanilla extract and sour cream until combined.
In a separate bowl, whisk together the flour, baking powder, cornstarch, and salt. Gradually fold this mixture into the wet ingredients.
Mix the melted butter and brown sugar until well blended for the topping.
Place a tablespoon of the brown sugar mixture in the bottom of each cavity of your prepared pan.
Top each tablespoon with a pineapple slice and a maraschino cherry.
Scoop spoonfuls of cookie dough on top of the pineapple slices, gently flattening each scoop.
Bake for about 25 minutes or until the edges are golden and the brown sugar is bubbly.
Allow cookies to cool in the pan for 10 minutes before inverting onto wax paper.
Let cookies cool completely before storing.