In a soup pot melt 2 tablespoons of butter over medium heat. Add the onions and sauté for 5 minutes, stirring frequently. Add 8 ounces of mushrooms and sauté until they have released their liquid and started to brown. Add the garlic and one tablespoon of chopped parsley, and cook one minute longer.
Stir in the flour untili it absorbs all remaining butter and liquid and cook for 1-2 minutes until lightly browned. Add in the broth gradually stirring to combine and ensure there are no lumps. Then pour in the milk or cream, salt and pepper. Cover and simmer over low heat for about 10 minutes stirring occasionally.
In the meantime cook the Tortelloni according to the package instructions. Melt remaining butter in a skillet and sauté remaining mushrooms until golden and softened, about 3-4 minutes.
Puré the soup using an immersion blender or a standing blender. Add additional broth to thin the cream, if desired. Add the Tortelloni and sautéed mushrooms to the soup. Divide into bowls and sprinkle with remaining parsley and a turn of freshly ground black pepper.