Preheat the oven to 350 degrees F. Line a 9-inch x 5-inch loaf pan with parchment paper, leaving it long enough to hang over the sides. Set aside.
Dice the apples and add them to a medium mixing bowl. Add 2 tablespoons of cake flour and mix to coat. Set aside.
In a small bowl, stir together 1/4 cup sugar and 2 teaspoons cinnamon until evenly combined. Set aside.
In a medium mixing bowl, stir together the cake flour, baking powder, cinnamon, and salt. Set aside.
In a large mixing bowl, stir the melted butter, sugar, and brown sugar together with a rubber spatula. Mix in the egg, milk, and vanilla until combined.
Add the flour mixture to the wet ingredients and mix until just combined. Add the apples and fold them into the batter. Don't overmix.
Pour half of the batter into the prepared loaf pan and spread into an even layer. Sprinkle 3 tablespoons of the cinnamon-sugar over the batter to create an even, thick layer. Pour the remaining batter into the loaf pan, spread it out, and top with the remaining cinnamon-sugar.
Bake for 40 minutes or until a toothpick inserted in the center comes out clean or with a couple of moist crumbs.
Remove from the oven and place on a wire rack to cool for at least 10 minutes before removing from the pan and slicing. Serve warm or at room temperature.
Notes
I like Granny Smith apples in this recipe, but you could use any kind of apple you like.