In a large bowl, whisk sweetened condensed milk, vanilla, key lime juice, and zest together until fully incorporated; set aside.
In a stand mixer fitted with a whisk attachment or a large bowl with a hand mixer, whip heavy cream until soft peaks form, then gradually add sugar and continue whipping until stiff peaks form.
Next, stir ⅓ of whipped cream into the wet ingredients, and then fold in the rest of the whipped cream until fully incorporated. Transfer ice cream into a freezer safe container.
Melt chocolate and drizzle over the ice cream, take a knife and swirl chocolate until desired look. Freeze for at least 2 days to harden.
When ready to serve, split one graham cracker sheet in a half and add a heaping scoop of ice cream on one half sheet and top with the other piece. Serve immediately. (You may make the sandwiches ahead of time and freeze.) Enjoy!
