Wipe the mushrooms with a wet cloth. Chop green onions coarsely, chop the garlic. Heat olive oil in a saucepan and add mushrooms. Cook, stirring occasionally, over medium heat for about 10 minutes. Add green onions and garlic and cook for another 3 minutes.

Add flour, stir and pour in the wine. Bring to a boil and remove from heat. Add 2/3 grated cheese, salt and pepper. Sprinkle with the remaining cheese and serve.