In a large pan, bring the water and chicken stock to a boil. Add 1 3/4 teaspoons of salt and the potatoes to the liquid. Cook until softened, about 15 to 20 minutes. Remove from the heat.
Meanwhile, in a skillet melt the butter over medium heat. Add the shallots and garlic. Cook for about 5 minutes. Add the wine to the skillet and reduce, about 2 minutes. Add the sautéed shallots, garlic and 1/4 teaspoon of salt to the potatoes. Puree with an immersion blender (food processor or blender would also work). Add the milk and stir well.
Place the soup back on the stove and heat over low. Add the mascarpone and red wine vinegar. Stir until the cheese is melted and incorporated with the soup. Serve warm with crouton gremolata (see below for recipe)