Line a 9x5 bread pan with wax paper and set aside.
In a large bowl, stir together condensed milk, key lime juice, and vanilla extract.
In a separate bowl (preferably a chilled metal bowl), whip the heavy cream with an electric mixer on high-speed until stiff peaks form.
Use a spatula to fold and stir the heavy cream into the condensed milk mixture until completely combined.
Pour about ½ of the ice cream mixture into the prepared bread pan, and spread it evenly.
Layer about ½ of your graham cracker mixture on top of this first layer.
Pour the remaining ice cream evenly into the bread pan, and then sprinkle the top with the remaining crumbs.
Cover the container well with clear wrap and freeze at least 6 hours (preferably overnight) before serving.