Preheat the oven to 350°F (175°C). Lightly grease a 9x9-inch baking dish.
Peel and dice 2 1/2 pounds apples into small pieces (you should have about 6 cups). In a large bowl, toss the diced apples with 1/4 cup lemon juice, 1/4 cup granulated sugar, 2 tablespoons cornstarch, 1/2 teaspoon ground cinnamon, and 1/2 teaspoon vanilla extract. Once fully combined, transfer the apple mixture to the prepared baking dish, including any juices left in the bowl.
In a medium bowl (or using a food processor), mix together 1 1/2 cups all-purpose flour, 3/4 cup brown sugar, and 1/2 teaspoon ground cinnamon. Add the cold, cubed butter and use a pastry cutter (or pulse in the food processor) to combine the mixture. The mixture should be crumbly, with small clumps of butter remaining.
Evenly sprinkle the crumble topping over the apples in the baking dish, covering them completely.
Bake for 40-45 minutes, or until the crumble topping is golden brown and the apple filling is bubbling. Serve warm.
Notes
Green apples like Granny Smith provide a nice tart flavor and are great for baking. Other yellow and red varieties that are good for baking include Golden Delicious, Honey Crisp, Braeburn, Jonathan, Fuji, and Pink Lady.