In a large bowl, whisk together heavy cream, half and half {or milk}, condensed milk, vanilla and salt.
In another bowl, beat together strawberry jam and softened cream cheese with a hand mixer until smooth. Slowly add a few tablespoons of the cream mixture and begin to beat and incorporate liquid a bit at a time {doing this slowly will help keep the mixture from becoming lumpy}; continue to add the liquid until fully incorporated.
Pour the mixture into an ice cream maker and churn according to manufacturer's directions. You'll want to get to a soft-serve consistency. Before finishing churning, toss in the diced strawberries to incorporate them into the mixture.
Scoop half of the ice cream into a freezer-safe container. Sprinkle about half of the crushed graham crackers over the ice cream. Scoop the rest of the ice cream into the container and top with the remainder of the crumbs.
Freeze for about 4-6 hours or until the desired scooping consistency is reached.