In a large mixing bowl, whisk together whole milk, organic cane sugar, and a pinch of salt until smooth and slightly frothy, about 2-3 minutes.

Gently fold in the heavy cream and key lime juice into the milk mixture using a spatula.

Pour the mixture into your ice cream maker and churn for about 25 minutes until it reaches a soft-serve consistency.

At the 20-minute mark, add in the crushed graham crackers while the ice cream is still churning, then let it churn for an additional 5 minutes.

Transfer the ice cream into a freezer-safe container, smooth the top, seal it, and freeze for at least 5-6 hours.

Allow the ice cream to sit at room temperature for a few minutes before serving, and optionally garnish with whipped cream or extra graham crackers.