In a large stock pot melt butter, add onion and cook over medium heat until onion is transparent. While onion cooks, place diced potatoes, carrots, water and chicken cubes in another large stock pot and bring to a boil. Cook until tender, about 10 minutes. Season with pepper to taste.
When vegetables are cooked, add flour to onion to make a paste. Add milk gradually: Mix well and heat over low until warm. Add vegetables and liquid. Stir thoroughly and heat for 5 to 10 minutes, over medium heat, stirring occasionally until mixture thickens slightly. Add parsley and thyme. Heat thoroughly and serve.