In a medium saucepan, melt the butter over medium heat. Add the diced apples, brown sugar, cinnamon, nutmeg, cloves, lemon juice, and salt. Stir to combine and coat the apples evenly.
Cook for 10-12 minutes, stirring occasionally, until the apples are tender but still hold their shape. Remove from heat and let cool completely.
In a large mixing bowl, use an electric mixer with whisk attachments to whip the cold heavy cream until stiff peaks form—about 3-4 minutes.
In a separate bowl, combine the sweetened condensed milk, vanilla extract, and ground cinnamon. Mix until well incorporated.
Using a rubber spatula, gently fold the sweetened condensed milk mixture into the whipped cream until just combined.
Reserve about 1/4 cup of the cooled apple pie filling for topping. Gently fold the remaining apple mixture into the cream base just until swirled throughout.
If using mix-ins, gently fold in half of the graham cracker crumbs and toasted nuts.
Pour half of the ice cream mixture into a 9x5-inch loaf pan or freezer-safe container. Drizzle with half of the caramel sauce (if using) and sprinkle with remaining graham cracker crumbs.
Add the remaining ice cream mixture and top with the reserved apple pie filling. Drizzle with remaining caramel sauce and sprinkle with remaining nuts.
Use a knife to swirl the toppings gently into the surface of the ice cream.
Cover the container with plastic wrap, pressing it directly onto the surface of the ice cream to prevent ice crystals from forming.
Freeze for at least 6 hours, preferably overnight, until firm.