Core and chop apples into chunks, around 1.2cm (1/2 an inch) in size. You can peel them, but I like them unpeeled. Set them aside.
Mix the melted butter, oil, sugars, sourdough starter, yogurt, vanilla, and eggs in a large bowl.
Whisk together flour, baking powder, baking soda, salt, and spices in a seperate bowl.
Fold through the dry ingredients, followed by the chopped apple pieces.
The batter will be quite thick. Don’t over-mix it.
Cold-fermenting (optional) – Cover the bowl tightly and place it in the refrigerator for up to 16 hours.
Preheat the oven to 350°F (180C). Line an 8.5x4.5 inch loaf pan with parchment paper. You could also use a larger 9x5 inch pan for a less high loaf.
Spoon into the prepared pan and bake for around 65-75 minutes until a skewer inserted into the center of the bread comes out clean. Let the apple bread cool in the pan for 15 minutes before removing it and allowing it to cool further on a wire rack.
When the apple bread has cooled to room temperature, mix together powdered sugar, cinnamon, and just enough milk to create a smooth and pourable paste. Drizzle this over the apple bread.
Notes
*The cup sizes given are for US-sized cups, which are smaller than metric cups; for best results, use a scale and measure in grams.