Preheat oven to 400F°.

Place apple chunks in a large baking dish so that they fit in a single layer place dollops of butter over top and sprinkle with brown sugar. Bake for 25-35 minutes, stirring occasionally, until the apples are soft enough to mash with a fork and the butter and sugar have caramelized. Remove from oven and set aside to cool. Place in a small container and refrigerate until chilled completely.

When the apples have cooled, whisk the egg yolks and sugar together in a large bowl until they are light yellow and fluffy. Set aside.

In a saucepan, combine the milk, cream, cinnamon, and cardamom. Cook over medium heat until the edges just begin to bubble, stirring occasionally.

While whisking the egg mixture, slowly drizzle in the milk mixture. Mix until combined. Return the egg mixture to the saucepan over medium heat and continue to cook until it is thick enough to coat the back of a spoon and registered 170F° on a candy thermometer.

Strain the mixture into a large bowl and stir in the vanilla extract, apple, and caramel sauce, and Applejack. Cool bowl over an ice bath to reduce the mixture’s temperature. Refrigerate until completely chilled, about 4-6 hours.

Process the mixture in your ice cream maker according to the manufacturer’s directions. Transfer half of the mixture to a container and drizzle half of the dulce de leche in. Using a butter knife, swirl around. Add the rest of the gelato and repeat with the dulce de leche. Freeze overnight.