Line an 8-inch square baking dish with aluminum foil with edges hanging over. Grease foil lightly with butter and set aside. Combine melted butter and graham cracker crumbs in a medium bowl. Stir with a fork until blended. Spread the crumb mixture into the bottom of the baking dish. Press down firmly to make an even layer.

In a medium saucepan over medium-low heat, combine the condensed milk and chocolate chips. Heat, stirring with a wooden spoon until the chocolate is melted and the mixture is smooth. Remove saucepan from heat and stir in vanilla and salt until blended. Pour the filling over the graham cracker crust and spread evenly with spoon.

Sprinkle the marshmallows evenly over the chocolate filling. Press them gently so that the marshmallows stick in the chocolate. Stick the remaining broken graham crackers into the chocolate mixture between marshmallows.