Place porcini mushrooms into a small container such as a coffee press, pour hot water over them and make sure the mushrooms are submerged. Let the mushrooms soak for at least 20 minutes, then lift them out. Inspect them and clean carefully if necessary. Finely chop the mushrooms. Remove any sediment from the liquid by pouring it through a fine-mesh strainer, and reserve.

Melt butter in large, heavy-bottomed Dutch oven over medium-low heat; when foaming subsides, add shallots and sauté, stirring frequently, until softened, about four minutes. Stir in garlic and nutmeg; cook until fragrant, about one minute longer. Increase heat to medium; add sliced mushrooms and stir to coat with butter. Cook, stirring occasionally, until mushrooms have started to brown, then add some salt and pepper. Continue to cook and stir until mushrooms have released their liquid, about seven minutes total. Reduce heat to medium-low, cover pot, and cook, stirring occasionally, until mushrooms have softened and released all liquid, about 20 minutes. Add chicken stock, water, and porcini mushrooms; cover and bring to simmer, then reduce heat to low and simmer until mushrooms are fully tender, about 20 minutes longer.

Pour soup into a large bowl. Rinse and dry Dutch oven. Puree soup in batches in blender until smooth, filling blender jar only halfway for each batch. Return soup to Dutch oven; stir in Madeira and cream and bring to simmer over low heat. Add cider vinegar, and season to taste with salt and pepper. Serve with sautéed mushroom garnish, if desired. (Can be cooled to room temperature and refrigerated up to 4 days. If making ahead, add cream at serving time.)

Optional Garnish: Heat butter in medium skillet over low heat; when foam subsides, add mushrooms. Cook, stirring occasionally, until mushrooms start to brown. Season with salt and pepper then cover pan and continue to cook, stirring occasionally, until mushrooms release their liquid. Uncover and continue to cook, stirring occasionally, until liquid released by mushrooms has evaporated. Sprinkle a portion of mushrooms over individual bowls of soup when serving.