In a large pot, melt the butter and olive oil over medium heat. Sauté diced onion, chopped carrots, and chopped celery for about 5-7 minutes until softened and fragrant.

Stir in minced garlic, dried rosemary, and thyme, and cook for an additional 1-2 minutes.

Add the diced chicken breast to the pot, stirring frequently until browned on all sides, roughly 5 minutes.

Sprinkle flour over the mixture, stirring well to coat everything evenly and cook for another minute.

Slowly pour in chicken stock and milk, stirring continuously to prevent lumps.

Incorporate diced Yukon Gold potatoes, bring to a boil, and then reduce to a gentle simmer.

Cover and let the soup simmer for 20-25 minutes, or until potatoes are tender.

Stir in low-fat cheddar cheese until melted and creamy.

Finally, stir in freshly chopped parsley and season with salt and pepper to taste. Serve hot.