In a large pot, melt butter with olive oil over medium heat. Add diced onions, chopped carrots, and sliced celery. Sauté for 7-8 minutes until softened.

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

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

Sprinkle flour over the mixture, stir well to combine, and cook for 1-2 minutes.

Gradually pour in chicken stock while stirring to avoid lumps. Bring to a boil.

Add diced Yukon Gold potatoes. Reduce heat and simmer for 20-25 minutes until tender.

Stir in shredded cheddar cheese until melted and integrated.

Season with salt and pepper to taste, garnish with parsley, and serve hot.