Melt the butter over low heat in a 3-quart saucepan and cook the onion in the butter until tender but not browned. Add the cubed chicken, potatoes, carrots, bouillon cubes, salt, pepper and water. Cover and cook, over high heat, until the mixture comes to a boil. Reduce the heat to low and simmer for 20 minutes or until the vegetables are tender. Meanwhile, combine the flour and 1/2 cup of the milk in a jar. Cover and shake until blended and smooth. Stir the flour mixture and remaining 2 cups of milk into the vegetable-chicken mixture. Cook over medium heat, stirring constantly, until the mixture boils and thickens. Remove from the heat and pour into a thermos jar or serve with the parsley sprinkled over.