Preheat your oven to 350°F (175°C) and lightly grease a medium baking dish.

Peel and slice the green apples into medium wedges, then place them in a large mixing bowl.

Add lemon juice, 1/2 cup brown sugar, white sugar, cinnamon, nutmeg, vanilla extract, and cornstarch to the apples, then toss well until evenly coated.

Transfer the apple mixture to the prepared baking dish and spread it into an even layer.

In a separate bowl, combine the flour, rolled oats, 1/4 cup brown sugar, and salt.

Add the cold cubed butter and mix with your fingers or a pastry cutter until the mixture looks crumbly.

Sprinkle the crumble topping evenly over the apple filling without pressing it down.

Bake for 35 to 40 minutes, or until the topping is golden brown and the apple filling is bubbling around the edges.

Let the dessert cool for 10 minutes before serving so the filling can set slightly.

Serve warm on its own or with a scoop of vanilla ice cream.