How to Make It
In a heatproof bowl, soak the dried porcini in the boiling water until softened, 20 minutes. Remove the mushrooms. Strain the liquid into a bowl through a sieve lined with a moistened paper towel. Rinse the porcini to remove any remaining grit and finely chop.
In a saucepan, melt the butter. Add the chopped porcini, button mushrooms, leeks, carrot, celery and rosemary and cook over moderate heat, stirring occasionally, until the vegetables are browned, 15 minutes. Add the chestnuts and stock and scrape up any browned bits stuck to the bottom of the pot. Add 3 cups of the strained porcini soaking liquid and season with salt and pepper. Bring the soup to a boil and simmer over moderate heat until the chestnuts are very tender, 30 minutes. Add the cream and let cool slightly. Puree in a blender in batches and keep warm.
In a skillet, heat the oil. Add the sliced porcini, season with salt and pepper and cook over moderately high heat until lightly browned, 6 minutes. Ladle the soup into bowls and garnish with the sautéed porcini.