In a small bowl, combine the brown sugar and cinnamon sugar. Set aside.
1 teaspoon cinnamon, ¼ cup brown sugar
In a medium-sized bowl, add the peeled and diced apples, granulated sugar, and apple pie spice. Mix until combined. Set aside at room temperature while you make the bread.
2 Granny Smith apples, 3 tablespoons granulated sugar, 1 teaspoon apple pie spice
For the Bread
Preheat your oven to 325°F. Line a 9x3 loaf pan with parchment paper, allowing the paper to hang over the sides. Spray with cooking spray and set aside.
In the bowl of a stand mixer fitted with the paddle attachment, or in a medium bowl with an electric hand mixer, cream the butter, oil, and granulated sugar on medium speed for 3 minutes, until light and fluffy.
½ cup unsalted butter, 1 tablespoon vegetable oil, ¾ cup granulated sugar
With a rubber spatula, scrape down the sides and bottom of the bowl. With the mixer on medium speed, add one egg at a time, creaming for 30 seconds after each addition. Scrape the sides after each egg. On low mix in the vanilla extract.
2 large eggs, 1 teaspoon pure vanilla extract
Add the cake flour, baking powder, salt, cinnamon, sour cream, and buttermilk. Mix on low just until incorporated and everything is evenly combined.
1 ½ cups cake flour, 1 teaspoon baking powder, ¾ teaspoon salt, ½ teaspoon cinnamon, ½ cup sour cream, 3 tablespoons buttermilk
Pour half the batter into the prepared loaf pan. Top with half of the cinnamon sugar mixture, then spoon in half of the apple mixture, avoiding any excess liquid.
Pour and level the remaining batter, then top with the remaining apple and cinnamon sugar mixture.
Bake at 325°F for 50-55 minutes. To check for doneness, insert a toothpick; it should come out with little to no crumbs. If batter is still on the toothpick, bake for an additional 5-10 minutes.
When the loaf is done, let it cool in the pan for 30 minutes.
For the Glaze
In a small bowl, mix the powdered sugar and water (or milk) until smooth.
1 cup powdered sugar, ¼ cup water or milk
Pour the glaze over the cooled bread. Serve warm or at room temperature.