Chill the ice cream bowl for at least 24 hours or until solid. You should not hear any water sloshing around when you shake the bowl. Combine the diced strawberries and ¼ cup of the granulated sugar in a medium saucepan.
Heat over medium and bring to a boil. Once boiling, reduce the heat to a simmer and cook for 10 minutes, until the sauce thickens slightly. Remove from the heat and cool to room temperature and then refrigerate until ready to use.
In a large bowl, add the cream cheese and the remaining ¾ cups of granulated sugar. Beat with an electric mixer until smooth.
Add heavy cream, whole milk, vanilla extract, and salt. Mix until smooth. Refrigerate for 30 minutes to make sure it’s very cold before churning.
Churn the ice cream mixture in the bowl of your ice cream machine according to your manufacturer’s instructions (mine took about 25 minutes), until it is thick and the consistency of soft-serve ice cream.
Spoon ⅓ of the ice cream base into a shallow container or a loaf pan. Drizzle ⅓ of the strawberry sauce over the ice cream. Sprinkle ⅓ of the graham crackers over the sauce.
Repeat two more times with remaining ice cream, strawberry sauce, and graham crackers. Lightly swirl with a knife to distribute.
Press plastic wrap or wax paper to the surface of the ice cream. Freeze for at least 4 hours, or until solid. Let sit at room temperature for about 5 minutes before serving.