Use the dried mushrooms or not, and substitute one of the following for the fresh mushrooms.
It’s easy enough to use oil and skip the cheese but a little trickier to duplicate the creaminess they lend to the dish. Replacing some of the stock or water with rice, oat, or nut milk (specifically hazelnut or almond) will help a lot, though they’re all slightly sweet and none is entirely neutral in flavor; soy milk, in fact, is too strong.