In a medium skillet, combine the apples, sugar, butter, and cinnamon over medium-low heat. Cook and stir for about 10 minutes until the apples have softened and released their juices. Cool completely, then chill thoroughly in the fridge.
2 Granny Smith apples, 1 1/2 Tablespoons salted butter, 3 Tablespoons granulated sugar, 2 teaspoons ground cinnamon
Whisk the milk, sugar, and cinnamon together in a large bowl for 2 minutes until the sugar has dissolved. Stir in the heavy cream and vanilla.
2 cups whole milk, 3/4 cups granulated sugar, 1 teaspoon ground cinnamon, 2 cups heavy cream, 2 teaspoons pure vanilla extract
Add the ice cream base mixture to the frozen bowl of an ice cream maker and churn for 20-25 minutes until the ice cream is thick and frozen to about the consistency of soft serve.
Add the apples and graham cracker pieces and churn for a few more minutes (or turn off the machine and stir them in be hand), until evenly incorporated.
5 cinnamon graham crackers
Transfer the ice cream to a freezer-safe container and place in the freezer for 4-6 hours until completely firm. Let sit out for 10 minutes before scooping to soften slightly.