Melt butter in a large pot over medium heat. Add garlic, onion, ginger and cook, stirring occasionally, until tender and fragrant, about 2-3 minutes. Turn the heat to medium high and add the fresh mushrooms. Season with salt and pepper, to taste, and cook until the mushrooms begin to brown, stirring occasionally.
Stir in wine then chicken broth and bring to a boil; reduce heat and simmer until slightly reduced, about 5 minutes. Stir in heavy cream.
In a small bowl, whisk together cornstarch and 2 tablespoons of water. Stir in mixture to the soup until slightly thickened, about 1-2 minutes; season with salt and pepper and honey, to taste. The soup should be quite thick, but if you prefer a thinner soup, add more chicken stock or add more cornstarch as needed if the soup is too thin.
Reheat soup before serving. Ladle into bowls and garnish with parsley. Serve hot or warm.