Preheat the oven to 350 degrees F.
Place the cake flour, all-purpose flour, sugar, baking powder, baking soda, and salt in a mixing bowl and whisk to combine.
Add the softened butter, beating on medium speed until the mixture resembles damp sand (about 2 minutes).
Stir in the egg until incorporated (about 1 minute).
Scrape the bottom and sides of the bowl with a silicone spatula, then add the sour cream, pineapple juice, and vanilla.
Mix the batter on medium-high speed for 60 to 90 seconds, to aerate the batter and build the cake's structure.
Pour the batter into the prepared pan, layering it over the fruit, and bake it until a toothpick inserted in the thickest part of the cake comes out clean (approximately 35 to 45 minutes).
Cool for 20 minutes in the pan, then invert onto a serving plate to cool completely before slicing.