Preheat your oven to 350°F (175°C). Lightly grease a 9x9-inch baking dish or similar-sized oven-safe dish.
In a large bowl, combine the sliced apples, granulated sugar, brown sugar, cinnamon, nutmeg, allspice, lemon juice, and cornstarch. Toss until the apples are evenly coated. Transfer the mixture to the prepared baking dish, spreading it out evenly.
In a medium bowl, mix together the oats, flour, brown sugar, granulated sugar, cinnamon, and salt. Add the cold butter cubes and, using a pastry cutter or your fingers, work the butter into the mixture until it resembles coarse crumbs. Stir in the chopped nuts if using.
Sprinkle the topping evenly over the apple mixture.
Bake in the preheated oven for 35-40 minutes, or until the topping is golden brown and the apples are tender when pierced with a fork.
Remove the crisp from the oven and let it cool for 5-10 minutes to allow the juices to settle.
Scoop warm apple crisp into bowls and top with a generous scoop of vanilla ice cream. Drizzle with caramel sauce if desired.