Preheat the oven: Preheat your oven to 350°F (175°C) and grease or line a 9×5-inch loaf pan with parchment paper.
Prepare the apple filling mixture: In a small bowl, toss the chopped apples with cinnamon and brown sugar until evenly coated. Set aside.
Mix the dry ingredients: In a large bowl, whisk together the flour, baking powder, cinnamon, nutmeg, and both sugars until well combined.
Mix the wet ingredients: In a separate bowl, whisk together the milk, sourdough discard, eggs, and vanilla extract until smooth.
Combine wet and dry ingredients: Gradually add the wet ingredients to the dry ingredients, stirring just until combined. Be careful not to overmix the batter.
Assemble the bread: Pour half of the batter into the prepared loaf pan, then sprinkle half of the apple filling mixture over the top. Pour the remaining batter on top, followed by the remaining apple mixture.
Bake the bread: Bake in the preheated oven for 55-65 minutes, or until a toothpick inserted into the center comes out clean. Allow the bread to cool in the pan for 10 minutes before transferring to a wire rack to cool completely.
Make the glaze: In a small bowl, whisk together the powdered sugar, milk, melted butter, and a pinch of salt until smooth.
Glaze the bread: Once the bread is cooled, drizzle the glaze over the top. Let it set before slicing and serving.