In medium sized skillet, heat 1 tablespoon of butter & oil until melted, then add onion and mushrooms. Cook until onions are translucent and mushrooms have softened, about 5 minutes, then add garlic and cook about 1 minute more.
Put in remaining butter and orzo and cook until orzo is lightly golden.
Then add broth, salt, and vermouth to the orzo mixture, bring to a boil, then turn down to a simmer, and cook stirring often until the orzo is soft and most of the liquid has absorbed, about 15 minutes.
Finally add parsley and cheese, mix well and plate.