Heat the olive oil in a heavy medium saucepan over medium-high heat. Add the onions and cook, stirring often, until softened, about 4 minutes. Add the mushrooms, salt, and pepper and cook until the mushrooms start to give off their liquid, about 3 minutes. Add the green onions, parsley, and garlic and cook, stirring often, until fragrant, about 1 minute. Stir in the stock and heavy cream and bring to a boil over high heat. Reduce the heat to medium-low and simmer until thickened to a sauce consistency, about 30 minutes.
Serve, or cover and keep warm until ready to use.
Yield: about 2 cups