Preheat your oven to 350°F (175°C). Grease a 9x5-inch loaf pan or line it with parchment paper.
In a large bowl, combine the rolled oats and milk. Let it sit for about 10 minutes to allow the oats to soak.
Add the applesauce, brown sugar, vegetable oil, eggs, and vanilla extract to the oat mixture. Mix until well combined.
In a separate bowl, whisk together the flour, baking powder, baking soda, cinnamon, and salt.
Gradually add the dry ingredients to the wet mixture, stirring until just combined. Fold in the diced apples and walnuts, if using.
Pour the batter into the prepared loaf pan and smooth the top.
Bake for 50-60 minutes, or until a toothpick inserted into the center comes out clean.
While the bread is baking, prepare the glaze by whisking together the powdered sugar, milk, and vanilla extract in a small bowl until smooth.
Once the bread is done, allow it to cool in the pan for 10 minutes before transferring it to a wire rack. Drizzle the glaze over the warm bread.
Let the bread cool completely before slicing.