In a food processor, working in batches if necessary, chop the fresh mushrooms to a coarse paste, stopping a couple of times to scrape down the sides of the bowl.
In a tall narrow stockpot, bring the fresh and dried mushrooms and water to a boil. Lower the heat and simmer, uncovered, for 30 minutes.
Strain through a fine-mesh sieve, and then through a damp-cloth-lined sieve. Use