Preheat your oven to 350°F and adjust the oven rack to the next-to-lowest position. Generously grease and flour a 10-cup bundt pan, ensuring all sides are well coated.
Start by dicing your apples into small, bite-sized pieces. You'll need about 2 cups of diced apples from two large Granny Smith apples.
In a large mixing bowl, whisk together the cake mix, all-purpose flour, brown sugar, ground cinnamon, and nutmeg until well combined.
Add the vegetable oil, eggs, vanilla extract, and buttermilk to the dry mixture. Using a mixer on medium speed, beat the ingredients for about a minute, ensuring everything is incorporated. Pause to scrape down the sides of the bowl, then beat for an additional minute.
Gently fold in the diced apples and transfer the batter into your prepared bundt pan, spreading it evenly.
Place the pan in the oven and bake for 40 minutes, or until a skewer inserted in the center comes out clean or with just a few crumbs. If the cake starts browning too quickly, lightly cover it with aluminum foil around the 20-minute mark.
Once baked, allow the cake to cool in the pan on a wire rack for approximately 10 minutes. Then, turn it out onto the rack to cool completely.