Step 1

Make the Crust: Preheat the oven to 350°F and set a rack in the middle position. Line a baking sheet with parchment paper.

Step 2

In a medium bowl, combine the graham cracker crumbs, melted butter, brown sugar, and salt. 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 ¼-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.

Step 3

Make the Ice Cream: In the bowl of an electric mixer, beat the cream cheese on medium speed until light and creamy, about 1 minute. Add the sweetened condensed milk and beat until completely smooth, 1 to 2 minutes. Add the heavy cream, lime zest, lime juice and salt, and beat until evenly combined, about 30 seconds.

Step 4

Assemble: Arrange half of the crust crumbles evenly over the bottom of an ungreased 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.