Line a 9-inch springform pan with parchment paper. Combine graham crumbs, sugar, salt and melted butter, then press firmly into the base and slightly up the sides. Chill for 20 minutes.
Beat the softened cream cheese until smooth. Gradually add the sweetened condensed milk and mix until creamy and lump-free.
Add the lime juice, lime zest and vanilla. Mix until evenly combined.
Whip the cold heavy cream until firm peaks form. Gently fold it into the lime mixture.
Spread the filling over the chilled crust. Cover and refrigerate for at least 6 hours, preferably overnight.
Slice with a warm, dry knife and garnish with lime zest, lime slices or whipped cream before serving.