Heat the oven to 350 degrees F. In a large mixing bowl, lightly whisk the egg yolks until smooth. Set aside.
In a medium, heavy-based saucepan, heat the brown sugar, milk, and cream over medium-high heat, stirring to dissolve the sugar. Scald the mixture (do not boil it) and remove it from heat.
While the cream mixture is heating, dissolve the sugar and water over low heat in a large, heavy-based saucepan increase the heat to high and boil the sugar until it=s amber in color. If the sugar starts to sputter, use a pastry brush dipped in water to wash down the sides of the pan. As soon as the sugar turns dark amber (like a old penny), carefully and slowly pour the hot cream into it, stirring the mixture. (The caramel will bubble as you add the cream, so use a long wooden spoon or whisk to combine them.)
Gently and slowly whisk the cream mixture into the egg yolks. Stir in the salt and vanilla. Strain the pudding and cool it in an ice bath or refrigerate until cool.
Skim of any air bubbles from the pudding mixture and divide the cool pudding mixture among 6 (6-ounce) ramekins. Set the ramekins in a shallow roasting pan and fill the roasting pan with hot water until it reaches halfway up the sides of the ramekins. Cover the pan with foil.
Bake the pudding until just set. Begin checking after 1 hour. When gently shaken, they should no longer look liquid; instead, the custard will move as one mass.
Allow the pudding to cool to room temperature in the water. Refrigerate the pudding for several hours or overnight before serving. The pudding will keep its dark color if refrigerated uncovered. It will taste no different but will look lighter if you cover it, which you should do (after it has cooled completely) if you have any strong flavored-food in you refrigerator