Add half of the melted butter to the bottom of a 9-inch cake pan and sprinkle with the brown sugar. Drain the pineapple rings and reserve 1/2 cup of the juice. Lay the pineapple rings on top in a concentric pattern, overlapping slightly. Place the cherries in the center of each of the pineapple rings.
Whisk together the remaining melted butter, reserved pineapple juice, eggs and sugar in a medium bowl until smooth. In another large bowl, whisk to combine the flour, cornmeal, baking powder and salt. Add the wet to the dry and mix together until just combined.
Pour the batter over the pineapple rings and bake on a sheet tray until a toothpick inserted in the center of the cake comes out clean, 40 to 45 minutes.
Cool the cake in its pan for 25 minutes. Run a knife along the edges to loosen. Place a plate over the top and carefully flip the cake out of the pan.