In a large pot, over medium heat, melt 2 tablespoons each of butter and olive oil. Add 1 diced onion, 1 cup of diced carrots, and 1 cup of diced celery. Sauté for 7-8 minutes until softened.

Stir in 2 minced garlic cloves and 1 tablespoon each of freshly chopped rosemary and thyme. Let the herbs bloom for another 1-2 minutes.

Add 1 pound of chicken breast pieces to the pot and cook for 5-7 minutes until browned on all sides.

Sprinkle 2 tablespoons of plain flour over the mixture, stirring well. Cook for about 1-2 minutes.

Gradually pour in 4 cups of low-sodium chicken stock while stirring, bringing the mixture to a gentle boil. Add in 2 medium waxy potatoes.

Reduce heat and let the soup simmer uncovered for 20-25 minutes, or until the potatoes are fork-tender.

Stir in 1 cup of low-fat cheddar cheese until melted. Taste and season with salt and pepper as needed.

Ladle the soup into bowls and garnish with fresh parsley if desired. Serve hot with bread or salad.