Preheat oven to 350°F (175°C) with rack in center. Lightly grease a 9x13-inch baking dish with butter or cooking spray.
Peel all apples, cut into quarters, remove the core, and slice into 1/4-inch thick slices or 1/2-inch chunks.
In a large bowl, combine sliced apples with flour, granulated sugar, brown sugar, vanilla, cinnamon, nutmeg, and salt. Toss until evenly coated.
Transfer apple mixture to prepared baking dish and spread into an even layer.
In a medium bowl, combine oats, flour, brown sugar, cinnamon, and salt. Whisk dry ingredients together until well mixed.
Add cold butter cubes to the dry mixture. Using a pastry cutter or fork, cut the butter into the mixture until it resembles coarse crumbs with pea-sized butter pieces.
Scatter the crumb topping evenly over the apple filling, pressing down slightly to help it adhere. Spread topping all the way to the edges.
Place baking dish on center oven rack. Bake for 45-50 minutes until topping is golden brown and filling is bubbling around the edges. Tent with foil if browning too quickly.
Remove from oven and let cool on wire rack for 15-20 minutes before serving. Serve warm with vanilla ice cream, whipped cream, or caramel sauce if desired.