Pre-heat the oven to 350F. Grease a 9-10 inch springform pan, both the bottom and sides of the pan. Take out the cream cheese and butter as well to soften for the frosting.
Peel the apples and dice into about 1/2 inch pieces and set aside.
In a small mixing bowl, mix together the flour, salt, baking soda, ground nutmeg and ground cinnamon and set aside.
Cook’s Note: Do not use a hand or stand mixer to make this cake dough. Due to the thick nature of this cake dough, it’s best to use a whisk for the eggs and then a large spoon to mix the batter.
In a large mixing bowl, beat 2 eggs with a whisk until light and fluffy, about 1-2 minutes.
To your whisked eggs, add sugar, vanilla and vegetable oil. Using a mixing spoon or spatula, mix all ingredients until combined.
Add the flour mixture into the egg mixture, stirring until combined. This mixture will be very thick, almost like a cookie-dough mixture. Fold the diced apples into the dough mixture and then scoop everything into your springform pan, smoothing out the top of the dough in the pan.
Bake the cake for 65-75 minutes. Start checking your cake at 65 minute mark. A toothpick inserted in the center of the cake should come out fairly clean when done. Once your cake is done, remove from the oven and let fully cool in the cake pan on a cooling rack.
Once the cake is fully cooled, it’s time to ice the cake. Gently remove the cake from the cake pan and turn out onto a cake stand or plate.
Use a hand or stand mixer to make the cream cheese icing: Whip the softened cream cheese and butter together on medium-high speed until smooth and combined, about 2-3 minutes. Add the vanilla extract and pinch of salt and mix for about a minute on low speed. Then add in 1 1/2 cups of the icing sugar and mix for about a 1 minute on medium speed, scraping down the sides as needed. Add in the rest of the icing sugar and mix for about another minute or so until smooth and fully combined.
Start icing the cake by placing a large dollop in the middle of the cake and then work your way outwards with a thin layer of icing over the entire cake. Then, continually add the rest of the icing to the cake until it’s evenly iced.