Butter the bottom and side of a 10-inch oven proof pie dish: set aside.
To make the crust: In a large bowl, combine the graham cracker crumbs, melted butter, sugar and salt. Using your hands, mix thoroughly until the ingredients come together. Press the graham cracker mixture over the bottom and up the sides of the pie plate. Chill the crust for at least 20 minutes.
Set the oven rack in the lower third of the oven. Preheat the oven at 350°F.
Place the chilled piecrust on a baking sheet and bake until lightly browned on the edge, and firm, 18 to 20 minutes. Remove to a wire rack and let cool while you make the filling. Do not turn off the oven.
To make the filling: In the bowl of a standing mixer fitted with the whisk attachment, beat the sweetened condensed milk with the yolks, salt and lime zest on medium speed until thick and pale, 2 to 3 minutes. Add the lime juice and beat until blended.
Pour the filling into the pie shell and bake, rotating the baking sheet about two-thirds of the way through the baking time, until the custard is set and just wiggle a bit in the center, 8 to 10 minutes. Remove to a wire rack and let cool for 15 minutes.
Refrigerate until well chilled.