Preheat oven to 350°F (175°C). Line two baking sheets with parchment paper. Pat pineapple rings completely dry with paper towels.

In a small saucepan over medium heat, melt butter and brown sugar together, stirring until combined and slightly thickened, about 2–3 minutes. Add cinnamon and a pinch of salt. Remove from heat.

Spoon 1 tsp of caramel glaze onto each prepared cookie spot on the parchment. Place one pineapple ring over each caramel pool and press a maraschino cherry into the center hole.

Whisk together flour, baking powder, baking soda, and salt in a medium bowl. In a large bowl, beat butter and both sugars until pale and fluffy, about 3–4 minutes. Add egg and vanilla, then mix in sour cream.

Gradually mix dry ingredients into the butter mixture on low speed until a soft dough forms. Do not overmix.

Drop a generous ball of dough (about 2 tbsp) over each pineapple ring. Press down gently to flatten the dough over the ring.

Bake 13–16 minutes until edges are set and tops look just barely underdone. Caramel underneath will be bubbling and golden.

While still hot (within 3–4 minutes), carefully flip each cookie upside down onto a wire rack lined with parchment. The pineapple and cherry will now face up. Cool 15 minutes before serving.