Preheat oven to 350 degrees.
Pour melted butter into 9" pie dish or tall metal cake pan. Using your fingers or a spatula, spread the butter onto the sides of the dish/pan.
Sprinkle the brown sugar over the butter mixture into an even layer. Place the pineapple slices over the bottom of the pan. Cut the leftover slices in quarters to fill in any of the large gaps near the edges of the dish/pan.
Place cherries in center of pineapple rings and in the remaining empty spaces.
To make the cake, in the bowl of a stand mixer or in a large mixing bowl with a hand mixer, beat butter and sugar for 2 minutes on medium speed, or until light and fluffy. Add eggs, mixing well after each addition. Add vanilla extract and beat for 15 seconds on medium speed.
In a separate mixing bowl, whisk together the flour, baking powder, and salt.
Alternate adding the flour, milk, and pineapple juice to the wet ingredients. Mix until combined. Pour the batter over the pineapple and cherry topping. Using a spatula, spread the batter into an even layer.
Place in the oven and bake for 30 minutes. At the 30 minute mark, loosely cover the cake with foil and continue to bake an additional 15-20 minutes, or until a toothpick inserted in the center comes out clean.
Remove from the oven and allow to cool to for 15 minutes before inverting onto a plate or cake stand. Let the cake cool for an additional 20 minutes before slicing and serving. This cake is best eaten on the day it is made, served with a big scoop of vanilla ice cream.