Preheat the oven to 350 degrees (F) and generously spray a 12-mold JUMBO muffin tin with non-stick cooking spray.

In a large mixing bowl, whisk the eggs until smooth. Add granulated sugar, brown sugar, and rum (or vanilla), and beat until smooth. Stir in pineapple juice. In a separate bowl, sift together flour, baking powder, cinnamon, salt, and cornstarch. Gradually add the dry ingredients to the wet ingredients, whisking until just combined. Avoid overmixing. Set the mixture aside.

For the topping, melt butter in a small saucepan over medium heat. Add brown sugar, rum, and salt, and cook for 1 minute while whisking constantly. Remove from heat.

Spoon 2 tablespoons of the topping mixture into the bottom of each muffin tin. Place a pineapple ring on top of each and a cherry in the center of each ring. Divide the cake batter evenly among the tins, filling each 3/4 of the way full. Bake for 20-22 minutes until the tops are puffed and golden brown, and a toothpick inserted in the center comes out clean.

Remove from the oven and let cool in the pan for 5 minutes. Use a knife to loosen the cakes, then place a wire cooling rack on top and quickly flip over. You can place the cooling rack on a sheet pan to minimize mess. Serve the cakes warm or at room temperature.