Step 1: Preheat your oven to 375°F (190°C). Grease a 9x13 inch baking dish or an 8x8 inch baking dish for a thicker crumble.
Step 2: Prepare the Apple Filling. In a large bowl, combine the peeled, cored, and sliced apples with granulated sugar, flour, cinnamon, nutmeg, cloves, and lemon juice. Toss gently until the apples are evenly coated. Set aside.
Step 3: Prepare the Caramel Sauce. In a medium saucepan over medium heat, melt the butter. Stir in the brown sugar, granulated sugar, and heavy cream. Bring to a gentle simmer, stirring constantly for 3-5 minutes, until the sugars are dissolved and the sauce thickens slightly. Remove from heat and stir in the vanilla extract and a pinch of salt. Be careful, as the sauce will be very hot.
Step 4: Assemble the Filling. Pour half of the warm caramel sauce over the apple mixture and toss gently to combine. Reserve the remaining caramel for drizzling later. Transfer the apple mixture to your prepared baking dish, spreading it out evenly.
Step 5: Prepare the Crumble Topping. In a separate large bowl, combine the flour, rolled oats, brown sugar, cinnamon, and salt. Whisk to combine. Add the cold, cubed butter to the dry ingredients. Using your fingertips, a pastry blender, or a fork, cut the butter into the mixture until coarse crumbs form, with some pea-sized pieces of butter remaining. Avoid overmixing.
Step 6: Top and Bake. Sprinkle the crumble topping evenly over the apple filling in the baking dish. Place the baking dish on a baking sheet to catch any potential drips. Bake for 45-55 minutes, or until the topping is golden brown, the apples are tender when pierced with a fork, and the filling is bubbly. If the topping browns too quickly, loosely tent with foil.
Step 7: Cool and Serve. Remove the crumble from the oven and let it cool for at least 15-20 minutes before serving. This allows the filling to set slightly. Drizzle the reserved warm caramel sauce generously over the top of the warm crumble. Serve warm with generous scoops of vanilla bean ice cream.