Heat the oven. Preheat to 350°F (175°C). Lightly butter a 9-inch square baking dish or similar 2-quart pan.
Prep the apples. Peel, core, and slice apples about 1/4 inch thick. Keep slices even so they cook at the same rate.
Toss the filling. In a large bowl, mix apples with granulated sugar, lemon juice, cinnamon, vanilla, cornstarch, and 1/4 teaspoon salt.
Stir until the slices look glossy and evenly coated.
Make the oat topping. In another bowl, combine oats, flour, brown sugar, and 1/4 teaspoon salt. Add cold butter cubes. Use your fingers or a pastry cutter to rub the butter into the dry ingredients until you have pea-sized clumps and sandy bits.
For extra crunch, leave some larger crumbs.
Add optional extras. Stir in nuts or dried fruit if using. Nuts add crunch; dried fruit sweetens the filling as it bakes.
Assemble. Spread the apple mixture evenly in the prepared dish. Sprinkle the oat topping evenly over the apples, covering them completely without packing it down too hard.
Bake. Place on a lined baking sheet (in case of bubbling).
Bake 40–50 minutes, until the topping is golden and the fruit juices are bubbling thickly around the edges.
Rest before serving. Let the crumble sit 10–15 minutes. This helps the juices set so each scoop holds together.
Serve. Enjoy warm with vanilla ice cream, whipped cream, or a spoonful of yogurt.