In small bowl, melt butter and set aside to cool. 

Peel, core and cut apples (preferably a variety of 4 types) into 1" chunks.

Preheat oven to 350 degrees. Generously butter the bottom of an 8" springform pan. Place on baking sheet with parchment or silicone mat underneath. 

In a small bowl, combine flour, baking powder and salt. 

In a medium / large bowl, whisk eggs until foamy. Add white and brown sugars and whisk until fully incorporated. Next, whisk in rum and vanilla. 

In alternating portions, whisk in flour blend and melted butter. Repeat until all ingredients are mixed together. 

Add apple chunks and use rubber scraper to stir them and coat liberally with the batter. Pour batter into greased springform pan and bake 50-60 minutes. 

Serve with a dusting of powdered sugar, or ice cream.