In a large pot, melt olive oil and butter over medium heat.

Add diced onions, carrots, and celery to the pot, cooking for 7-8 minutes until softened.

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

Incorporate diced chicken breast and cook for 5-7 minutes until browned.

Sprinkle flour over the mixture, stirring well for about 1 minute.

Gradually pour in milk while stirring until the mixture is smooth.

Add diced potatoes and chicken stock, stir well, and bring to a gentle boil.

Reduce heat to low and let the soup simmer for 20-25 minutes.

Once potatoes are cooked, stir in cheddar cheese until melted.

Fold in chopped parsley, salt, and pepper.

Ladle soup into bowls and garnish with extra parsley if desired. Serve hot.