In a small heavy saucepan, boil the water with the sugar, without stirring, until a golden caramel color results. Remove the pan from the heat and carefully add the vinegar and balsamic vinegar down the side of the pan. Stir the mixture over moderate heat until the caramel is dissolved, about 3 minutes. Remove the pan from the heat.
In a heavy saucepan cook the morels in butter, stirring, over moderate heat until liquid from morels is evaporated, about 5 minutes. Transfer the morels with a slotted spoon to a bowl and reserve. Add the shallots and the cayenne to the pan and cook, stirring, until golden. Stir in the wine and boil until reduced to about 1 cup, about 15 minutes.
Add the stock and reserved morel soaking liquid (if using dried morels) and reduce to about 1 1/4 cups, about 15 minutes. Remove the pan from heat and stir in caramel mixture. Add the morels to sauce with salt and pepper to taste. You can serve the sauce as is or processed in a blender or food processor.
