In a large mixing bowl, whisk together the heavy cream, whole milk, granulated sugar, vanilla extract, ground cinnamon, and nutmeg until the sugar is fully dissolved.

Pour the mixture into an ice cream maker and churn according to the manufacturer's instructions until it reaches a soft-serve consistency.

Gently fold in the chopped apple pie filling and crushed graham crackers.

Transfer the mixture to an airtight container and freeze for at least 4 hours or until firm.

Before serving, let the ice cream sit at room temperature for about 5-10 minutes to soften slightly for easier scooping.