Combine 1/2 cup of cold water with flour to create a slurry mixture in a bowl and whisk until well blended. Set aside.
Pour remaining water and milk into a large pot and slowly bring to a boil.
Add celery, onion, mushrooms, chicken bouillon, thyme, fresh pepper, frozen vegetables and return to boil.
Cover partially and simmer on low until vegetables are soft, about 20 minutes.
Remove lid, add potatoes and cook until soft, about 5 minutes.
Add chicken, and slowly whisk in the slurry mixture, stirring well as you add.
Cook another 3-5 minutes, until soup thickens.
Adjust with salt and pepper to taste, serve.