Preheat the Oven and Prepare the Pan: Preheat the oven to 350°F (175°C). Position a rack in the center.

Lightly grease a 9 × 13-inch metal baking pan. For easier removal, line the bottom and long sides with parchment paper, leaving a small overhang.

Toast the Pecans: Spread the pecans on a small baking sheet. Toast in the preheated oven for 5–7 minutes, stirring once, until fragrant and slightly darker.

Transfer them to a plate and let them cool before chopping. Keep the oven at 350°F (175°C).

Prepare the Apples: Peel and core the apples, then cut them into approximately ½-inch pieces.

Measure 3 cups (about 360 g) after chopping: Keep the pieces fairly uniform so they soften at the same rate. Set them aside while you prepare the batter.

Combine the Dry Ingredients: In a medium bowl, whisk together the flour, baking powder, baking soda, kosher salt, cinnamon, and nutmeg.

Whisk thoroughly so the leavening agents and spices are evenly distributed.

Mix the Wet Ingredients: In a large bowl, whisk the eggs, granulated sugar, and brown sugar for about 1 minute, until smooth and evenly blended.

Add the vegetable oil and vanilla extract: Whisk again until the mixture looks glossy and uniform.

Make the Batter: Add the dry ingredients to the wet mixture. Fold gently with a rubber spatula until only a few streaks of flour remain.

The batter will be thick: Avoid overmixing, which can make the finished cake tough.

Fold in the Apples and Pecans: Add the diced apples and chopped toasted pecans. Fold until the fruit and nuts are evenly distributed and no dry flour remains.

The batter will become very chunky and may appear to contain a large amount of apple compared with batter. This is expected.

Transfer to the Pan: Spread the batter evenly in the prepared 9 × 13-inch pan.

Use the spatula to push the batter into the corners and level the surface.

Make sure the apple pieces are distributed rather than piled in one area.

Bake the Cake: Bake at 350°F (175°C) for 40–45 minutes. The top should be golden brown and spring back lightly when touched near the center. A toothpick inserted into the cake portion should come out clean or with a few moist crumbs, but no raw batter.

Avoid inserting the toothpick directly into a piece of apple, which may make the cake appear underbaked.

If the edges brown too quickly, loosely cover the cake with aluminum foil during the final 10 minutes.

Cool the Cake: Transfer the pan to a wire rack and let the cake cool for at least 45 minutes before slicing.

The crumb is delicate while very warm and becomes easier to cut as it cools.

For the cleanest slices, allow the cake to cool completely.

Add the Optional Topping: Once the cake has cooled, dust the surface lightly with the optional powdered sugar.

Use a fine-mesh sieve for an even coating: Skip the powdered sugar if you prefer a more rustic finish or plan to store the cake for several days.

Slice and Serve: Serve at room temperature or slightly warm. The cake is flavorful on its own, but it can also be served with lightly whipped cream or vanilla ice cream.