Heat butter and oil in a large nonstick skillet over medium heat. Add garlic and mushroom, and saute until lightly browned, about 10-15 minutes. Set aside.
Place carrot and chicken broth in a pot. Cover the pot and cook over medium heat until carrot is tender, about 15-20 minutes.
Dissolve flour in the cold milk and add to soup. Then add the parsley, mushroom, Worcestershire sauce, salt & pepper. Cook covered for 10 minutes. Then add the cream and cook for 1-2 more minutes (don't let boil). Taste and adjust seasoning. Serve with lemon juice on the side.