Beat the butter, sugar, and vanilla sugar until creamy. Add the eggs one at a time and mix until smooth.
Add the self-rising flour, salt, and cinnamon; mix until the dry ingredients are incorporated.
Peel the apple, remove the core, and cut into small cubes. Toss the cubes with a little flour, this keeps them from sinking to the bottom while baking.
Fold the apple pieces into the batter. Pour the batter into a greased and floured baking pan. If you like, sprinkle some coarse cinnamon sugar on top.
Bake for about 60 minutes at 175°C/345°F (top and bottom heat) until golden brown.
Insert a skewer into the cake; if it comes out clean, the cake is done. Let it cool slightly in the pan before transferring it to a rack to cool completely.
How to store
Store the apple cinnamon loaf cake outside of the fridge, wrapped in aluminum foil for up to a week. Freezing is a good option too. It will keep in the freezer for up to three months.