Line a 9x9-inch square baking pan with parchment paper, leaving plenty of overhang on all sides so you can easily lift the bars out later.

Pulse the graham crackers in a food processor or blender until they form fine crumbs. Pour the melted butter over the crumbs and pulse a few times until incorporated. You may need to mix with a silicone spatula until well combined.

Transfer half (2 cups) of the crumb mixture into the prepared pan. Set the other half of the crumb mixture aside. Use the flat bottom of a measuring cup to press the crumbs firmly into the bottom of the pan to create a flat base. Place the pan in the freezer to set while you prepare the filling.

In a stand mixer fitted with the whisk attachment (or in a bowl with an electric hand mixer), add the heavy cream. Mix on medium-high speed for 1-2 minutes until soft peaks form. Pour in the sweetened condensed milk, lime zest, lime juice, vanilla extract, and salt and mix on low speed until no streaks of sweetened condensed milk remain.

Remove the pan from the freezer. Pour the ice cream filling directly over the chilled graham cracker base, smoothing the top into an even layer with a silicone spatula. Cover the pan loosely with plastic wrap and freeze for 1-2 hours, or until the surface of the ice cream layer is firm enough to the touch that the top layer of crumbs won't sink into it when you press them down.

Remove the pan from the freezer and sprinkle the remaining graham cracker crumb mixture evenly over the surface of the semi-frozen ice cream layer. Use the flat bottom of a measuring cup to firmly but gently press the crumbs into the ice cream so they adhere well and form a solid top crust.

Return the pan to the freezer and freeze for about 2 hours (or up to 24 hours), until the ice cream is completely frozen.

Remove the pan from the freezer. Grip the parchment paper overhang and lift the entire block cleanly out of the pan onto a cutting board. Use a long, sharp knife to slice the block into 9 large or 16 small squares. For clean cuts, wipe the knife blade with a hot, damp cloth between each slice.

Serve immediately, or wrap individual bars in plastic wrap and store them in an airtight container in the freezer for up to 2 weeks.