Preheat the oven to 350 °F. Grease a 9x11 baking dish and set aside.
In a bowl, mix the brown sugar and eggs until smooth. Stir in baking powder, vanilla, cinnamon, and salt. Then, pour in the melted butter and milk, and mix until combined. Add the walnuts and oats and stir. Pour the oatmeal mixture into your prepared baking dish.
In a skillet, melt the butter or coconut oil over medium-high heat. Add the apples and a pinch of salt, and sauté until they start to brown and caramelize, about 5 minutes. Spread the apples evenly over the oatmeal layer in your dish.
In a separate bowl, mix together the butter, flour, sugar, salt, cinnamon, and nutmeg using a pastry cutter or your hands until the mixture becomes coarse crumbs. Stir in the oats and nuts. Sprinkle this crisp topping over the apples.
Bake for 30-40 minutes, until the crisp topping turns golden brown. Let it cool for about 10 minutes before digging in.