Preheat oven to 350F. Place rack to middle position. Place cupcake liners in two 12-cup muffin pans. (You will need four more so you can wait until a batch of cupcakes bake before lining with the remaining ones.)
In a stand mixer with a paddle attachment, mix butter, oil, and sugar on high speed, until very pale and fluffy, about 4minutes. Meanwhile, sift flour, baking powder, soda, and salt in a large bowl.
Reduce speed to medium and add eggs, one at a time combining well after each addition, scraping down the sides of the bowl as needed.
Reduce speed to low and slowly add sifted dry ingredients. Mix until just combined. DO NOT OVERMIX.
Lastly, add sour cream, milk, vanilla, and rum. Scrape down sides of bowl and mix until just combined. Turn off mixer.
Spoon 1 teaspoon of melted butter into the bottom of each liner. Top butter with 1 teaspoon of brown sugar. Finally spoon 1 teaspoon of crushed pineapple over brown sugar and spread out on bottom of liner.
Using an ice cream scoop, add cake batter to each liner over the pineapple. The liner should be three-quarters full.
Bake until light golden brown, a toothpick inserted into the center of the cupcakes come out clean, about 18-20 minutes.
Allow cupcakes to cool in the pan for 10 minutes, then remove from the pan and place them on a cooling rack to cool completely, about 20 minutes.