Heat olive oil in a large pot over medium heat. Add onions, carrots, and celery; sauté until softened, about 7 minutes. Add garlic and cook for an additional 2 minutes.
Increase heat to medium-high. Add chicken pieces and season with salt and pepper. Cook until chicken is browned on all sides.
Sprinkle flour over the chicken and vegetables, stirring to coat. Slowly add chicken broth and milk, stirring continuously. Add cubed potatoes. Bring to a boil, then reduce heat to a simmer. Cook for 20-25 minutes or until potatoes are tender.
Stir in cheddar cheese until melted. Season with salt and pepper to taste. Garnish with fresh parsley before serving.