Step 1: In a small saucepan, combine the strawberries, 1/4 cup of sugar, and lemon juice. Simmer over medium heat for 10-15 minutes until the mixture thickens into a jam-like consistency. Let it cool completely.
Step 2: In a large mixing bowl, beat the softened cream cheese with the remaining 1/2 cup of sugar until smooth and airy.
Step 3: Slowly whisk in the heavy cream, whole milk, and vanilla extract until the mixture is well combined and no cream cheese lumps remain.
Step 4: Pour the cream mixture into your ice cream maker and churn according to the manufacturer's instructions, usually about 20-25 minutes.
Step 5: While the ice cream churns, mix the graham cracker crumbs with melted butter and a pinch of salt in a small bowl to create the cheesecake 'crust' clusters.
Step 6: In the last 2 minutes of churning, add half of the cooled strawberry reduction and the graham cracker clusters to the ice cream maker.
Step 7: Transfer the churned ice cream to a freezer-safe container, swirling in the remaining strawberry reduction with a knife for a marbled effect. Freeze for at least 4-6 hours before serving.