Preheat oven to 350°F (175°C) with a rack in the center. Grease an 8x8-inch baking dish with cooking spray or butter, coating the corners.
Wash the apples, quarter and core them, then dice into 1/2-inch pieces. Leave the skin on for extra fiber and color, and set aside a few thin slices for the top if desired.
In a large bowl, stir together the rolled oats, baking powder, 1 3/4 teaspoons cinnamon, salt, and half of the walnuts until evenly combined.
In a medium bowl, whisk the milk, applesauce, maple syrup, eggs, vanilla, and slightly cooled melted butter for about 30 seconds until smooth.
Pour the wet mixture into the dry ingredients and stir gently until all oats are moistened, then fold in the diced apples. Let the batter rest for 5 minutes so the oats absorb liquid.
Stir the batter once more and pour it into the prepared dish, spreading into an even layer. Top with reserved apple slices, remaining walnuts, and the last 1/4 teaspoon cinnamon.
Bake for 35 to 40 minutes until the top is golden brown and the center is set and springs back slightly. If the center looks loose, bake 5 more minutes and check again.
Cool on a wire rack for 10 minutes so the oatmeal firms up, then cut into 9 squares and serve warm with milk, maple syrup, or your favorite toppings.