Prepare the Apples. Peel and core the apples, then cut them into small, evenly sized pieces. Keeping the pieces small makes them easier to mix into the ice cream later.
Caramelize the Apples. Melt the butter in a skillet over medium heat. Add the diced apples, 3 tablespoons of sugar, and 1 teaspoon of cinnamon. Cook for 8–10 minutes, stirring occasionally, until the apples are tender, golden, and lightly caramelized. Remove from the heat and allow them to cool completely before adding them to the ice cream.
Prepare the Graham Crackers. Place the graham crackers in a ziplock bag and gently crush them into small pieces. Leave some larger chunks for texture rather than crushing everything into fine crumbs. Set aside.
Make the Ice Cream Base. In a large mixing bowl, combine the whole milk, 1¼ cups of sugar, salt, half-and-half, vanilla extract, whipping cream, and 2 teaspoons of cinnamon. Whisk until the sugar has dissolved and all ingredients are thoroughly combined. The mixture should be smooth and creamy.
Churn the Ice Cream. Pour the prepared mixture into your ice cream maker. Churn according to the manufacturer’s instructions, approximately 20–25 minutes, or until the ice cream reaches a thick, soft-serve consistency.
Add the Apples and Graham Crackers. Once the ice cream has thickened, gently fold in the completely cooled caramelized apples and graham cracker pieces. Distribute them evenly throughout the ice cream without overmixing.