Set your oven to 350°F (175°C). Grease a 9x5-inch loaf pan so the bread doesn’t stick.
In a small bowl, mix the chopped apples with brown sugar and cinnamon. Set them aside.
In a large bowl, whisk together the flour, white sugar, baking powder, baking soda, salt, cinnamon, and nutmeg.
In another bowl, whisk the sourdough discard, milk, oil, egg, and vanilla until smooth.
Pour the wet mixture into the dry ingredients and stir gently. Don’t overmix—the batter should be a little lumpy.
Pour half of the batter into the loaf pan. Add half of the apple mixture on top. Pour in the rest of the batter, then add the remaining apples. Press the apples in gently and swirl everything slightly with a knife.
Bake for 55 to 65 minutes. Check with a toothpick—if it comes out clean, it’s done. Let the bread cool for about 15 minutes.
Mix powdered sugar, milk, and vanilla in a small bowl. Once the bread is cool, drizzle the glaze over the top.