Arrange a rack in the middle of the oven and heat to 350°F (175°C). Grease and flour 2 (8-inch or 20-centimeter) round cake pans and set aside.

Sift together the flour, baking powder, baking soda, salt, cinnamon, and cardamom and set aside.

In the bowl of a stand mixer fitted with the paddle attachment, beat the oil, sugar, and lemon zest on medium speed for 2 minutes. Turn the mixer to medium-low and add the eggs and egg yolk one at a time. Stop the mixer and scrape down the bowl.

Turn the mixer to low and add the flour mixture in three batches, alternating with the buttermilk, beginning and ending with the flour mixture. Mix on medium for no more than 30 seconds after the last streaks of the dry ingredients are combined. Fold in the apples.

Evenly divide the batter between the prepared pans. Bake for 24 to 26 minutes, or until a toothpick inserted into the center of the cakes comes out clean. Let them cool on a wire rack for 10 to 15 minutes before removing the cakes from their pans.

Place the egg whites and sugar in the bowl of a stand mixer. Whisk them together by hand to combine.

Fill a medium saucepan with a few inches of water and place it over medium-high heat. Place the mixer bowl on top of the saucepan to create a double boiler. The bottom of the bowl should not touch the water. Whisking intermittently, heat the egg mixture until it registers 145° to 155°F (63° to 68°C) on a candy thermometer, or is hot to the touch.

Once hot, carefully fit the mixer bowl onto the stand mixer. With the whisk attachment, beat the egg white mixture on high speed for 8 to 10 minutes, until it holds medium-stiff peaks. When done, the outside of the mixer bowl should return to room temperature and no residual heat should be escaping the meringue out of the top of the bowl. Stop the mixer and swap out the whisk attachment for the paddle.

With the mixer on low speed, add the butter, a few tablespoons at a time, and then add the vanilla. Once incorporated, turn up the mixer speed to medium-high and beat until the buttercream is silky smooth, 3 to 5 minutes.

Remove all but 2 ½ cups of the buttercream from the bowl (save the remaining for another use). Add the sour cream, honey, and cardamom to the mixer and mix until combined.

Heat a heavy-bottomed skillet over medium heat. Stirring intermittently with a wooden spoon, dry-roast the oats and walnuts (if using) until fragrant and slightly browned, 5 to 8 minutes.

Add the honey, butter, nutmeg, and salt and stir to evenly coat the oats. Cook, while stirring, for 3 to 5 minutes more. Remove from the heat, spread out the mixture on a piece of parchment paper, and let it cool.

Once the cakes have completely cooled, halve them horizontally to create 4 even layers. Level the cakes and choose which layer will be at the bottom. Place it on a cake plate or serving dish.

Spread on a quarter of the buttercream with an offset spatula. Top with the next layer of cake and repeat two times more with the buttercream, ending with the fourth layer. Frost the top of the cake with the remaining buttercream. Garnish the top with a generous handful of the skillet oat crumble. (Sprinkle any leftover crumble over yogurt.) Drizzle with honey, if using.