Prepare the Apple Filling:
Preheat your oven to 375°F (190°C).
In a large bowl, combine the sliced apples, granulated sugar, brown sugar, cinnamon, nutmeg, lemon juice, vanilla extract, and flour (or cornstarch). Mix gently until the apples are evenly coated.
If using, stir in the chopped nuts.
Pour the apple mixture into a 9-inch square or round baking dish. You can also use individual ramekins.
Make the Crumble Topping:
In a separate bowl, combine the flour, oats, brown sugar, cinnamon, and salt.
If using melted butter: Pour the melted butter over the dry ingredients and mix with a fork until the mixture forms clumps and resembles coarse crumbs. Be careful not to overmix.
If using cold butter: Cut the cold butter into small cubes. Add the butter to the dry ingredients and use a pastry blender or your fingertips to cut the butter into the flour mixture until it resembles coarse crumbs. This method creates a slightly more “biscuit-like” crumble.
Assemble and Bake: