In a medium saucepan, combine the heavy cream, milk, half the sugar, and salt. Warm over medium heat until steam rises from the surface, but don't let it boil.
Whisk the egg yolks with the remaining sugar in a separate bowl until pale yellow and slightly thickened.
Slowly pour about 1 cup of the hot cream mixture into the egg mixture while whisking constantly to temper the eggs.
Return the tempered egg mixture to the saucepan with the remaining cream mixture. Cook over medium-low heat, stirring constantly, until the mixture thickens enough to coat the back of a spoon (about 5-7 minutes or 170°F).
Remove from heat and pour through a fine-mesh sieve into a clean bowl. Stir in the vanilla extract, cover with plastic wrap (pressing it directly onto the surface), and refrigerate until completely chilled, at least 4 hours or overnight.
For the apple filling: In a medium saucepan, melt the butter over medium heat. Add the diced apples, brown sugar, cinnamon, nutmeg, cloves, and lemon juice. Cook for 8-10 minutes until the apples are tender but still hold their shape. Transfer to a bowl and refrigerate until completely cooled.
For the caramel sauce: Place sugar in a heavy-bottomed saucepan over medium heat. Watch carefully as it melts and turns amber (about 4-5 minutes), gently swirling the pan to ensure even melting.
Once the sugar has completely melted and turned a deep amber color, carefully add the butter and stir until melted. Slowly drizzle in the heavy cream while stirring constantly (mixture will bubble). Add sea salt, continue stirring for about 1 minute, then remove from heat and let cool completely.
If using a pre-made pie crust, bake according to package instructions, then let cool completely and break into small, bite-sized pieces.
Pour the chilled ice cream base into your ice cream maker and churn according to the manufacturer's instructions, usually 25-30 minutes. In the last 5 minutes of churning, add half of the cooled apple pie filling and pie crust pieces.
Transfer one-third of the churned ice cream to a freezer-safe container. Drizzle with one-third of the caramel sauce and top with one-third of the remaining apple filling and pie crust pieces. Repeat the layers twice more.
Use a knife to gently swirl the layers together. Cover the surface with parchment paper, seal the container, and freeze until firm, at least 2 hours or overnight.