Preheat oven to 350 degrees. Add butter from topping ingredients into bundt pan and place in oven to melt for about two minutes.
Meanwhile, add flour, sea salt, and baking powder to a bowl and whisk to combine. In another bowl, combine ½ cup pineapple juice from the can of slices, milk, butter, brown sugar, vanilla, and egg and mix until uniform.
Add wet mixture to dry and stir until batter is uniform and no dry pockets remain. Set aside.
Carefully remove pan of melted butter from oven and mix in brown sugar to create the topping. Arrange pineapple slices and cherries in pan as shown. Carefully pour cake batter over top.
Place pan on middle rack of oven and bake for 45-50 minutes or until a toothpick inserted into multiple parts of the cake comes out clean.
Remove cake from oven and let sit for about 10 minutes then invert onto a platter.
Using a wooden skewer or toothpick, pole several holes in all sides of the cake. Place cake back in pan and poke more holes into bottom of cake.
Combine rum syrup ingredients in a small bowl and mix vigorously until uniform. Then slowly pour rum syrup over top of cake, allowing it to flow into the poked holes.
Allow cake to soak for about an hour then invert it again onto a plate and serve warm. Do not refrigerate cake during this step.
This cake is best served immediately after the rum has had time to soak in so I don't recommend making it ahead. If you do need to make it in advance, bake the cake, remove it from the pan after 10 minutes, and allow it to fully cool then cover it and place in the refrigerator. Before serving, allow it to come to room temperature then make the rum sauce and resume the recipe steps from there.