Preheat the oven to 350 degrees F. Lightly grease a 10x7 or 8x8 baking dish with butter.
In a bowl, combine the oats, brown sugar, cinnamon, baking powder, and salt.
In a large bowl, whisk together the milk, eggs, melted butter, and vanilla.
Add the dry ingredients and the diced apples to the wet ingredients. Stir until well combined.
Bake the oatmeal for 40 to 50 minutes. (See notes)
Allow it to cool about 10 minutes before serving.
Notes
40 minutes will result in wetter looser oatmeal.
50 minutes will result in drier and more firm oatmeal. You may find that you need to cover the oatmeal with foil for the last 10 minutes of baking if it's getting too dark.
Store leftovers in an airtight container in the fridge. Use up within 5 days.