Create a slurry by combining 1/2 cup of the cold water with flour in a medium bowl and whisk until well blended. Set aside. In a large pot, saute the celery and onion in the olive oil until beginning to soften. Add the mushrooms and continue to saute until all are soft. Pour remaining water and milk into a large pot and slowly bring to a boil. Add chicken bullion, thyme, fresh pepper, frozen vegetables and return to a boil. Partially cover and simmer on low until vegetables are soft, about 10 minutes. Remove lid, add potatoes and chicken if raw cook until soft, about 5 minutes. If using cooked chicken, add and slowly whisk in slurry, stirring well as you add. Cook another 5 tp 7 minutes, until soup thickens and flour cooks. Adjust salt and pepper to taste and serve.