Pour 1 1/3 cups water and the bourbon into a medium saucepan and set over high heat. Carefully pour the sugar directly into the center so none of it splashes up the sides of the pan. Bring to a boil and cook until the sugar starts to turn brown. Do not stir the pan. If necessary, gently swirl the pan to help melt all the sugar.
Once the sugar turns a deep, rich brown, remove the pan from the heat and pour in the heavy cream slowly and carefully. It will splatter a little and the caramel will seize up if the cream is added too quickly. Add the butter, salt and vanilla. Swirl the pan until the butter dissolves completely and evenly into the caramel sauce. The butter makes it shiny and rich.
Drizzle a little caramel sauce into each of the tall milkshake glasses.
Combine the ice cream, milk and the remaining caramel sauce in the blender, reserving a little caramel on the side to garnish the tops of the milkshakes at the end. Blend until smooth and pour into the glasses. Top each with a little whipped cream, a pinch of sea salt and a drizzle of the reserved caramel sauce.
Caramel can be made up to a week ahead of time. Keep it in the refrigerator until needed. Use any leftover for topping apples, ice cream or pancakes.
This recipe has been updated and may differ from what was originally published or broadcast.