Heat the butter and oil in a large pot or dutch oven over medium heat. Once the butter has melted, add the onion, carrot and celery with a pinch of salt. Cook, stirring often, until they have softened up. Add the garlic and cook a minute or so more, until fragrant. Then stir in the flour and cook for an additional minute or two.

Increase the heat to med-high. Stir in the broth, about a cup at a time, making sure the flour and onion mixture blends in smoothly and theres no lumps. Then stir in the cream, seasonings and chicken. Let the soup come up to a low boil.