In a 3-quart pot, heat the butter and oil over medium heat. Add the onion and celery; sauté until the veggies are softened but not browned, about 5 to 7 minutes. Add the shredded carrot, garlic, and bay leaf, and sauté until the carrot starts to soften and the garlic is fragrant, about 1 to 2 minutes.
Stir in the flour and cook 2 minutes, then gradually whisk in the chicken stock, milk, Worcestershire, Dijon, hot sauce, salt, and pepper. Stirring frequently, bring the soup up to a boil over medium heat, then turn heat down and simmer 10 minutes.
Turn the heat off and whisk in the cheese, and then stir in the chicken. Taste and season with additional salt, pepper, and hot sauce as desired.
Serve with the blue cheese and scallion sprinkled on top, along with additional hot sauce if desired.