Preheat your oven to 375°F and grease your 9-inch baking dish with butter or a light coating of oil. This step keeps the finished oatmeal from clinging stubbornly to the sides once it's baked. Set the dish aside while you prepare your ingredients.
In your large mixing bowl, combine the oats, baking powder, cinnamon, and salt. Stir them together until they're evenly distributed throughout the mixture. This ensures every bite has the same balanced flavor once it's baked.
In your medium bowl, whisk together the milk, egg, maple syrup, melted butter, and vanilla extract. Whisk until the mixture looks smooth and fully combined, with no streaks of egg remaining. This forms the custardy base that holds the whole bake together.
Pour the wet mixture into the bowl with your dry ingredients, then add the diced apple and walnuts. Stir everything gently until it's just combined, being careful not to overmix. You want the apple pieces distributed evenly throughout the batter.
Pour the mixture into your prepared baking dish and spread it into an even layer. Bake for 30 to 35 minutes, until the top turns golden brown and the center feels set when you press it gently. Let it cool for a few minutes before slicing and serving.