Heat oil and butter in a saute pan large enough to fit mushrooms. When oil and butter start to sizzle add shallots to pan saute 1 minute, then add garlic. Saute another minute, when soft but not brown, add mushrooms. Saute mushrooms until brown, liquid released and evaporated. Add marsala and cook a couple minutes to almost evaporated. Add stock, thyme and continue to cook until reduced by half. Add heavy whipping cream and simmer until sauce thickens and again is reduced by half. Add green onions and 1/4 cup parmesan cheese. Salt and pepper to taste.