Preheat the oven to 350°F (175°C) and lightly grease the baking dish with butter.
In a large bowl, stir together the rolled oats, quick oats, baking powder, cinnamon, nutmeg, and salt.
In a separate bowl, whisk together the milk, applesauce, maple syrup, eggs, melted butter, and vanilla extract.
Pour the wet ingredients into the dry mixture and stir gently to combine. Fold in the diced apples, raisins, and chopped nuts.
Transfer the mixture to the prepared baking dish and spread evenly.
Bake for 35–40 minutes, until the top is golden and the center is just set.
Let cool for 5–10 minutes before slicing and serving. Serve warm with maple syrup or yogurt if desired.