In a heavy medium saucepan, heat the oil over medium-high heat. Add the shallots and cook, stirring often, until soft and fragrant, 2 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 thestock 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, 20 to 30 minutes.
Serve, or cover and keep warm until ready to use.
Yield: about 2 cups