Chill the ice cream bowl for at least 24 hours or until solid. You should not hear any water sloshing around when you shake the bowl.
Place brown sugar and butter in a medium saucepan. Stir until the butter is melted and the brown sugar and butter are combined.
Add apples and 1 teaspoon of the ground cinnamon, stir to coat the apples.
Cook, for 10-15 minutes, stirring occasionally, until the apples are tender. Place in a bowl and refrigerate until chilled.
In a large bowl, combine the heavy cream, whole milk, granulated sugar, salt and remaining 1 teaspoon of ground cinnamon.
Whisk for 2-3 minutes, until the sugar is dissolved into the mixture. You should not feel any grit if you rub the mixture together between two fingers.
Churn the ice cream mixture in the bowl of your ice cream machine according to your manufacturer’s instructions (mine took about 25 minutes), until it is thick and the consistency of soft-serve ice cream.
In the last two minutes, add the chopped snickerdoodle cookies and churn until evenly distributed.
Spoon half of the ice cream into a shallow container or a loaf pan. Top with half of the apple mixture. Repeat with remaining ice cream and apples.
With a knife, swirl the apple mixture into the ice cream base.
Press plastic wrap or wax paper to the surface of the ice cream. Freeze for at least 4 hours, or until solid. Let sit at room temperature for about 5 minutes before serving.