In a large sauce pan, heat the oil over medium heat. Add the onion and celery and cook for 2-3 minutes. Add the garlic and cook for 1 minute. Add the carrots and potatoes, season with salt and pepper. Sauté for 5 minutes. Add in 1 cup of the chicken broth and the 1 cup of water and simmer for about 5 minutes until the vegetables are tender.
In a stock pot, add the butter and melt over medium heat. Then whisk in the flour. Take a couple of minutes, whisking occasionally, letting the roux simmer and bubble. Slowly whisk in the remaining 3 cups of chicken broth and add the water. Add the frozen corn, peas, bay leaf, parsley, poultry seasoning, pepper and salt.
Add the vegetables to the stock pot and bring to a low boil. Stir in the milk and cream. Add the chicken. Let simmer until all the vegetables are cooked through. Serves 6.