3 oz. dried shiitake mushrooms
3 C. boiling water
1 lb. white mushrooms
1 1/2 tsp. salt
about 8 scallions, cut in half
6 cloves garlic, peeled and left whole
2 or 3 sprigs fresh thyme (or 1/3 tsp. dried)
few drops sherry or vermouth, if you have any on hand
Rinse the dried shiitakes, place them in a bowl, pour boiling water over them, and let them soak for at least 20 minutes. Strain the mushrooms over a second bowl, pressing out and saving all the liquid. Pull off and discard the stems, then place the shiitakes and fresh mushrooms together in a food processor and pulse until they're in small pieces. Or chop them up with a knife into very small pieces.
Put all the mushrooms in a soup pot with the reserved mushroom-soaking liquid. Add 4 additional cups of water, salt, scallions, and thyme. Bring to a boil, then reduce heat to a simmer, cover, and cook gently for about 40 minutes.
Line a strainer with two layers of cheesecloth or a coffee filter. Strain the liquid into a pot (or a storage container, if you're saving it for later or freezing it). If it's appropriate to the recipe, you can put some of the mushrooms back into the broth or save them for another use. Stir in just a drizzle of sherry or vermouth, if you like.