Preheat the oven to 375 degrees Fahrneheit and spray a 9 x 9-inch cake pan with oil or grease lightly with butter.
Whisk together oats, baking powder, salt, cinnamon and nutmeg in a medium or large bowl.
Wash, peel, core and dice the apples.
Melt one tablespoon of butter in a skillet, then add ⅓ of diced apples (1 apple) and ¼ teaspoon cinnamon. Cook undisturbed for 5 minutes on medium heat, then give the apples a stir and cook 5 more minutes or until lightly browned. Turn off the heat and set aside.
In a small bowl of measuring cup whisk together plant milk, applesauce, egg and vanilla.
Add wet ingredients to dry and stir until combines. Stir in raw diced apples.
Transfer the oatmeal batter into the prepared cake or casserole pan and press lightly to form one even layer.
Top the oatmeal with cooked apples distributing evenly. Scoop up the browned butter from the skillet and add with the apples.
Bake for 40-45 minutes until the oatmeal is firm to touch and the edges are lightly browned.