There is a unique twist to this recipe, one which not everyone will be able to match. It's the use of preserved mustard tuber. Maybe by the time I've finished this post I'll be able dredge up an alternative. The tuber adds a wonderful extra touch of "umami," that extra dimension of taste which is mentioned more and more.
Here is wikipedia's definition of umami: Umami, popularly referred to as savoriness, has been proposed as one of the basic tastes sensed by specialized receptor cells present on the human and animal tongue. Umami is a loanword from Japanese meaning "flavor" or "taste" (noun) in that language. In English, however, "brothy", "meaty", or "savory" have been proposed as alternative translations. In as much as it describes the flavor common to savory products such as meat, cheese, and mushrooms, umami is similar to Brillat-Savarin's concept of osmazome, an early attempt to describe the main flavoring component of meat as extracted in the process of making stock.
Here's a variation to do without the mustard tuber. Reconstitute 1/2 of the shiitakes in a combo of soy sauce and fish sauce. Heat just enough of it to cover the 'shrooms and then add some or all of the liquid to the soup. Also, puree a few of the shiitakes along with the button mushrooms. That should work pretty well.
8-10 reconstituted shiitake mushrooms (depending on size)
8 oz. button mushrooms
1 tbsp olive or vegetable oil
2 tbsp butter, divided
1/2 medium onion, chopped
1/2 tsp onion powder
1/2 tsp garlic powder
1/2 packet of preserved mustard tuber
2 tbsp corn starch, dissolved in water
2 15 oz. cans beef stock
1/2 cup heavy cream
salt and white (or black) pepper, to taste
1 scallion, white and green parts, chopped (garnish)
chopped parsley (garnish)
Slice the shiitakes and the button mushrooms. Heat the oil and butter in a soup pan until the butter's foam subsides.
Saute the onion and mushrooms until starting to brown, about 10 minutes over medium heat. Season with onion and garlic powders and some pepper. Don't add salt yet.
Remove about 1/2 of each of the types of mushrooms and set aside.
Put the remaining mushroom onion mixture and the corn starch and the mustard tuber (if using) into a food processor. Add about a cup of the beef stock and puree completely. Return all this to the soup pan and add the remaining beef stock. Taste and adjust seasonings according to your preference. Add back the reserved mushrooms. Add the cornstarch and simmer, stirring occasionally for 4-5 minutes. Add the cream. Bring to a simmer and simmer very slowly for about 10 minutes.
Taste another time for seasoning, adding a bit of salt if you think necessary. Serve garnished with scallion and parsley.