Begin by peeling and cutting the apples into ¼-inch cubes. The apple pieces won't shrink much during baking, so you don’t want the pieces to be too large.
In a medium bowl, stir the apples with the brown and granulated sugar and let the mixture sit until the sugar dissolves. This should take about 15 minutes.
Place all dry ingredients (i.e., flour, cinnamon, baking powder, baking soda, and salt) in a large bowl and whisk to combine.
Add the apples and any released juices, the eggs, and oil to the large bowl. Stir well until combined. Fold in the roasted pecans. Do not mix the cake batter with a stand or hand mixer. That will cause the apple pieces to break apart in the batter.
At this point, it will look like there are too many apples for the cake batter. This recipe is supposed to be full of chunky apple pieces. I promise there is enough batter to make this cake!
Pour the batter into the prepared pans and bake the Apple Spice Cake for approximately 30 minutes or until a toothpick inserted into the center of the cake comes out clean. If you think the toothpick hit an apple, insert it again in a different location to confirm the cake portion is cooked.
Let the cakes cool on a wire rack for 15-20 minutes and then turn the cakes out onto the rack to cool completely to room temperature.