In a large mixing bowl, beat the cream cheese until it's light and fluffy.
Add the sweetened condensed milk and vanilla extract to the bowl and mix 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 until fully incorporated.
Pour a small amount of the mixture into a chilled freezer-safe container.
Add strawberry puree (see recipe) to the ice cream mixture, and use a butter knife to swirl it around.
Crumble the graham crackers into the ice cream mixture, making sure it's evenly distributed.
Repeat the layering process, adding more ice cream mixture, strawberry puree, and graham cracker crumbs until you reach the top of the container.
Cover the container with plastic wrap and lid, and freeze for at least 6 hours, or overnight, until the ice cream is firm.