Preheat the oven to 350°F. Grease and line the bottom of two 8" cake pans with parchment.
Sift the flour, baking powder, baking soda, salt, cinnamon, and cardamom together in a bowl and set aside.
Beat together the oil, sugar, and lemon zest with the paddle attachment for about 2 minutes.
Lower the mixer speed to medium-low and add in the eggs and egg yolk one at a time. Scrape down the bowl.
Lower the speed again to low and add the flour mixture in three batches, alternating with the buttermilk — begin and end with the flour mixture.
After the last of the flour disappears into the batter, bump up the speed to medium and beat for 30 seconds. Don't overmix!
Fold in the diced apples.
Divide evenly between the cake pans and bake for about 20-30 minutes, or until the top looks golden and a cake tester comes out clean. However, because of the fresh apples, probe in a few places near the center of the cake if your tester comes out wet just in case you happened to spear an apple chunk.
Let the cake cool on a wire rack in its pan for 15 minutes before turning it out to cool completely directly on the rack.