Preheat oven to 350 degrees F. Spray a 9-inch cake pan with baking spray. Drain the pineapple (reserving ¼ cup of the juice) and pat the pineapple rings and maraschino cherries dry on paper towels.
Combine the brown sugar and melted butter in a small bowl, then spread into the bottom of the prepared pan. Arrange seven of the pineapple slices in the bottom of the pan, then cut the others in half and place them along the sides of the pan, filling in holes with the maraschino cherries.
In a large bowl, beat the butter, granulated sugar, and brown sugar until creamy and light. Add the egg, sour cream, milk, pineapple juice, and vanilla and mix again, scraping down the sides of the bowl. The batter may start looking curdled, but that's okay.
Add the flour, baking powder, and salt, then mix until combined. The batter will be fairly thick. Spoon the batter over the fruit and spread it into an even layer.
Bake for 40-45 minutes, just until a toothpick inserted into the center of the cake comes out clean and the cake is golden brown on top. Let cool for 5-10 minutes before turning out onto a serving plate. Loosen the sides of the cake from the pan first by running a thin, sharp knife around the edges. Then place your serving plate upside down on top of the cake pan before flipping both over. The cake will drop right out of the pan, although you may have a piece of fruit or two that likes to stick. If so, just lift it out and place it back on top of the cake.
Serve warm or at room temperature.