In a small saucepan, add the strawberries, sugar, and vanilla. Bring mixture to a boil, reduce heat and simmer for about 5 minutes or until sauce thickens. Let cool completely. You can speed this up by chilling in the refrigerator.
Ice Cream:
Whip the cream in a bowl until soft peaks form. Transfer to another bowl. Some cream might still be in the bowl but no need to wash it.
Add the cream cheese and sweetened condensed milk to the bowl and beat until smooth. Gently fold in the whipped cream.
Fold in the graham crackers and transfer mixture to a freezable container allowing for some room for it to expand when it freezes. Drizzle the strawberry mixture on top and swirl with a knife. Sprinkle additional graham cracker chunks on top if desired. Freeze for 8 hours or until firm.