Heat olive oil and butter in a large pan over medium heat.
Add the mushrooms and cook until golden and their liquid evaporates, about 8 minutes.
Stir in the shallots and garlic, cooking until fragrant, about 2 minutes.
Pour in the Marsala wine and let it simmer until reduced by half.
Lower the heat, then stir in the cream and thyme. Simmer gently until the sauce thickens, 8 to 10 minutes.
Season with salt and black pepper.
Toss with pasta or serve over rice. Garnish with parsley before serving.