Preheat the oven to 375°F and grease an 8×8-inch baking dish.
Prepare the apples: In a large bowl, place the chopped apples, flour, brown sugar, lemon juice, vanilla extract, cinnamon, nutmeg, and salt. Toss to coat the apples, then spread evenly in the prepared baking dish.
Make the topping: In a medium bowl, whisk together the oats, flour, brown sugar, cinnamon, and salt. Use two forks, a pastry cutter, or your hands to work in the butter until the mixture is crumbly. Sprinkle evenly over the apples.
Cover the baking dish and bake for 35 to 40 minutes, or until the apples are bubbling. Uncover and bake for 10 to 15 more minutes, or until the apples are tender and the topping is golden brown and lightly crisp.
Remove from the oven and let cool for at least 10 minutes before serving.