Preheat the oven to 350°F (175°C). Lightly grease an 8x8-inch or 9x9-inch baking dish.
In a large mixing bowl, whisk together the milk, eggs, applesauce, maple syrup or honey, and vanilla extract.
Add the rolled oats, baking powder, cinnamon, nutmeg, and salt. Stir until the ingredients are evenly combined.
Fold in the chopped apples and walnuts or pecans, if using.
Pour the oatmeal mixture into the prepared baking dish and spread it into an even layer.
Bake for 35–40 minutes, or until the center is set and the top is lightly golden.
Allow the baked oatmeal to cool for several minutes before serving. Enjoy warm with extra milk, cream, or a drizzle of maple syrup.