In a large pot, melt the butter with the olive oil over medium heat. Add the diced onions, carrots and celery, and sauté for 7-8 minutes.
Stir in the garlic, rosemary, and thyme, and cook for another 1-2 minutes,
Add the chicken breast pieces to the pot and cook until the chicken is browned on all sides.
Sprinkle the plain flour over the chicken and vegetables, stirring well to coat.
Slowly pour in the milk, a little at a time, stirring constantly to ensure a smooth mixture and prevent lumps.
Add the diced potatoes, then pour in the chicken stock, stirring to lift any bits stuck to the bottom of the pot.
Bring the mixture to a boil, then reduce the heat to low. Allow the soup to simmer for about 20-25 minutes or until the potatoes are tender.
Add the low-fat cheddar cheese to the pot, stirring until it's fully melted into the soup.
Stir in the fresh parsley, then season with salt and freshly ground black pepper to taste.