Heat the oven to 350°F (175°C). Grease a 9x13-inch pan and line the bottom with parchment.
In a medium bowl, whisk the flour, baking soda, baking powder, salt, cinnamon and nutmeg.
In a large bowl, whisk the oil with both sugars until smooth. Whisk in the eggs one at a time, then the sour cream and vanilla.
Add the dry ingredients and fold with a spatula until just a few streaks of flour remain. Fold in the apples. The batter will be very thick.
Spread the batter evenly in the pan. Stir the topping sugar and cinnamon together and sprinkle over the top.
Bake for 45 to 55 minutes, until the top is deep golden and a toothpick in the center comes out clean or with a few moist crumbs.
Cool in the pan on a rack for at least 30 minutes before cutting.