Preheat the oven to 350 degrees F (180 degrees C) and set a rack in the middle position. Line a baking sheet with parchment paper.
In a medium bowl, combine the Graham Cracker Crumbs (1 cup), Unsalted Butter (4 tablespoon), Dark Brown Sugar (1/4 cup), and Salt (1 pinch). Using a spoon first and then your fingers, mix until evenly combined, making sure to break up any lumps of brown sugar.
Press the crust into an even 1/4-inch layer on the prepared baking sheet. Bake until golden around the edges, 7 to 8 minutes.
Let cool, then use a spoon to break into chunks. Set the crust aside while you make the filling.
To start, zest and juice the Lime (3).
In the bowl of an electric mixer, beat the Cream Cheese (8 ounce) until light and creamy, about 1 minute.
Add the Sweetened Condensed Milk (14 ounce) and beat until completely smooth, 1 to 2 minutes.
Add the Heavy Cream (1/4 cup), lime zest, lime juice and Salt (1 pinch). Beat until evenly combined, about 30 seconds.
Arrange half of the crust evenly over the bottom of an 8-by-4-inch loaf pan.
Pour the ice cream mixture over top.
Then cover with the remaining crust crumbles. Cover with plastic wrap and freeze until completely firm, at least 8 hours or overnight.