01 - Combine strawberries, 3 tablespoons sugar, and lemon juice in a saucepan. Cook over medium heat for 5–7 minutes until berries are soft and syrupy. Let cool, then mash slightly. Refrigerate until fully chilled.
02 - Beat cream cheese until smooth in a medium bowl. Gradually whisk in milk until well combined. Add heavy cream, ¾ cup sugar, vanilla, and salt. Mix until smooth and creamy.
03 - Cover the mixture and refrigerate for at least 2 hours, or until thoroughly cold.
04 - Mix graham cracker crumbs, melted butter, and 1 tablespoon sugar in a small bowl. Spread on a parchment-lined baking sheet and bake at 350°F for 8–10 minutes until golden. Let cool.
05 - Pour the chilled base into an ice cream maker. Churn according to manufacturer's instructions, typically 20–25 minutes, until thick and creamy.
06 - Layer the churned ice cream in a freezer-safe container, alternating with spoonfuls of strawberry swirl and graham cracker crumble. Swirl gently with a knife for a marbled effect.
07 - Freeze for at least 4 hours, or until firm. Let soften slightly before scooping and serving.