For the salted caramel milkshake: Combine the ice cream, milk, and caramel sauce in a blender and blend until smooth.
For the salted caramel sauce: In a heavy-bottomed saucepan, combine the sugar and water over medium-low heat until the sugar dissolves. Increase the heat and bring to a boil, without stirring. If necessary, use a wet pastry brush to wash down any crystals on the side of the pan. Boil until the syrup is a deep amber color, about 5 to 6 minutes. Remove the sugar from the heat and carefully whisk in the heavy cream. The mixture will bubble. Stir in the unsalted butter, and salt. Transfer the caramel to a dish and cool.
This recipe will last in the refrigerator up to 2 weeks. Reheat before serving.