In a small saucepan, combine chopped strawberries, sugar, and lemon juice. Cook over medium heat for 8-10 minutes until strawberries break down.
Mix cornstarch with 1 tablespoon of water and stir into the strawberry mixture. Cook for 2 more minutes until thickened. Remove from heat and let cool completely.
In a large mixing bowl, beat the softened cream cheese until smooth and creamy.
Add the sweetened condensed milk and vanilla extract to the cream cheese, beating until well combined.
In a separate bowl, whip the heavy cream until stiff peaks form. Gently fold the whipped cream into the cream cheese mixture.
Pour half of the ice cream base into a 9x5-inch loaf pan. Drop spoonfuls of the cooled strawberry sauce over the top and sprinkle with half of the graham cracker crumbs.
Pour the remaining ice cream base over the top. Add the remaining strawberry sauce and use a knife to swirl it through the ice cream. Sprinkle with the remaining graham cracker crumbs.
Cover tightly with plastic wrap and freeze for at least 8 hours or overnight before scooping and serving.
Notes
Freezing time takes at least 8 hours or overnight before scooping and serving.