Prepare the Apple Filling: In a medium bowl, combine diced apples, sugar, cinnamon, and nutmeg (if using). Let the mixture sit for 10 minutes while you prepare the bread batter.
Whisk Dry Ingredients: In a large bowl, whisk together both flours, baking powder, baking soda, cinnamon, and salt.
Combine Wet Ingredients: In a separate bowl, whisk together eggs, sugar, sourdough discard (or starter and water), melted butter, and milk.
Combine Wet and Dry Ingredients: Pour the wet ingredients into the dry ingredients and gently fold with a spatula until just combined. Be careful not to overmix.
Fold in Apples: Gently fold the diced apples and their juices into the batter.
Prepare Baking Pan: Preheat oven to 350°F (175°C) and grease a loaf pan (9×5 inch).
Pour Batter: Pour the batter into the prepared loaf pan.
Bake: Bake the bread for 50-60 minutes, or until a toothpick inserted into the center comes out clean.
Cool and Glaze (Optional): Let the bread cool in the pan for 10 minutes before transferring it to a wire rack to cool completely. While the bread cools, prepare the glaze (optional) by whisking together powdered sugar and milk until smooth. Drizzle this glaze over the cooled bread.