In a large pot over medium heat, melt equal parts of butter and olive oil until shimmering, about 2-3 minutes. Add diced onions, carrots, and celery to the pot, stirring occasionally. Sauté these ingredients for 7-8 minutes until the vegetables soften.

Stir in minced garlic and let it cook for 1-2 minutes until aromatic. Add in the chicken breast pieces, cooking for about 5-7 minutes until they are browned on all sides.

Sprinkle plain flour evenly over the chicken and vegetable mixture, stirring to coat everything thoroughly, about 1-2 minutes.

Gradually pour in the milk while stirring continuously to prevent lumps. Add the diced potatoes and chicken stock, mixing well. Bring the mixture to a boil over medium-high heat.

Let the soup simmer for 20-25 minutes, stirring occasionally, until the potatoes are tender. The soup will thicken beautifully.

Stir in the low-fat cheddar cheese until it melts completely. Mix in freshly chopped parsley and season with salt and pepper to taste.

Ladle the warm soup into bowls and garnish with additional parsley, if desired. Serve hot.