Preheat the oven to 350°F (175°C). Grease a 9 x 13-inch (23 x 33 cm) metal baking pan. Line the bottom and two long sides with parchment paper, leaving a slight overhang for easier removal.

Peel and core the apples, then cut them into pieces approximately 1/2 inch (1.25 cm) wide. Measure 3 cups (360 g) after cutting. Keep the pieces fairly uniform so they soften at the same rate.

In a medium bowl, whisk together the flour, cinnamon, baking soda, baking powder, and salt. Break up any compacted flour and make sure the leavening is distributed evenly.

In a large bowl, whisk the eggs, oil, brown sugar, granulated sugar, and vanilla for about 1 minute. The mixture should look smooth, glossy, and evenly blended, without visible streaks of egg.

Add the dry ingredients to the wet mixture: Fold with a flexible spatula until only a few small flour streaks remain. The batter will be thick and may require firm folding rather than whisking.

Fold in the diced apples and optional toasted walnuts or pecans. Continue folding until the fruit is evenly distributed and no dry flour remains. The batter should look heavily filled with apples but still hold together around them.

Transfer the batter to the prepared pan: Spread it evenly into the corners and smooth the surface. Press any exposed apple pieces lightly into the batter so they do not dry out during baking.

Bake on the center rack for 42 to 48 minutes. The top should be deep golden, the center should spring back lightly when pressed, and the edges should begin pulling slightly away from the pan.

Insert a toothpick into the center in an area without a large apple piece. It should come out clean or with a few moist crumbs. Wet batter indicates that the cake needs another 3 to 5 minutes.

If the top becomes dark before the center is baked, place a loose sheet of aluminum foil over the pan and continue baking. Do not seal the foil tightly around the edges.

Place the pan on a wire rack and let the cake cool for 30 minutes. The crumb will be delicate while hot because of the amount of fruit.

Use the parchment overhang to lift the cake from the pan, or leave it in the pan for serving. Cool for another 30 minutes, until the center is no longer warm.

Dust the cooled cake with powdered sugar, if using. Cut it into 15 pieces with a sharp knife, wiping the blade between cuts if moist crumbs collect on it.