Place mushrooms in a small bowl and pour one cup of boiling water over the mushrooms and set aside. Place a large sauté pan, over medium heat. Add the EVOO, onion and shallot and a small sprinkle of kosher salt. Sauté slowly until the onions are caramelized, being careful not to burn them. This should take approximately 5 minutes until they are golden brown.
Drain the mushrooms well reserving the soaking liquid. Chop lightly if the pieces are large. Add the mushrooms and thyme leaves to the sauté pan. Sauté for another minute and then add the Marsala wine, scraping up any browned bits.
Bring a large pot of salted water to a boil.
Reduce the wine by half and add the mushroom stock. Continue cooking over medium heat until liquid is again reduced by half. Add in the balsamic, and then the heavy cream stirring well to combine. Allow to simmer for an additional minute or two, to allow the sauce to thicken. Season well with kosher salt and a generous amount of fresh ground pepper.
Boil your pasta in the salted water, cook until al dente.
Add the cooked, drained pasta to the sauté pan. Toss it with the sauce and allow it to simmer in the sauce for an additional minute.
Serve with grated fresh Pecorino Romano cheese.