Combine hulled strawberries, sugar, and cornstarch in a medium saucepan over medium heat. Mash them up with gently. I prefer this mixture to be chunkier. If you want it smooth, blend it first before heating.
Cook, stirring frequently, until the berries break down and thicken into a sauce. Remove from the heat and cool completely.
With a standing mixer and whip together the heavy whipping cream on medium speed. When the cream starts to come together turn it up a notch and thicken more (about 5 minutes total to get it thick)
Next, add in sweetened condensed milk, soft cream cheese and vanilla. Keep whipping until well combined.
Using a rubber spatula, transfer contents from standing mixer bowl to a freezer safe container. Use an 8x8 or a 9x5 loaf container.
Sprinkle crumbled graham crackers and add blobs of the Strawberry jam around the dish, use a knife to gently “swirl” the jam around.
Cover and let sit in the freezer flat for at least 5 hours. If you want the ice cream to be firmer, leave for 8 hours.
