Add the butter to a medium-size pot over low heat and sweat the onion and celery while occasionally stirring. for about 4 to 6 minutes or until tender. They should not be browned at all.
Stir in the flour until it is completely mixed in.
While constantly whisking, pour in the chicken stock and turn the heat to high to bring to a boil.
Once the mixture is boiling, add in the thyme, peppercorns, and parsley, and then turn the heat down to low and simmer for 30 minutes.
Season with salt and pepper, and strain through a chinois. To make cream of chicken, see notes. Serve or store.
Chef Notes:Make-Ahead: You can make this recipe up to 3 days ahead of time. Keep cool until ready to use.How to Store: Cover and keep in the refrigerator for up to 5 days. You can freeze this, but the sauce may break, and you will need to rethicken it.How to Reheat: Add the desired amount of velouté to a small size saucepot and heat over low heat until hot. You may need to rethicken it using a small amount of roux.You can also add 1 finely minced garlic clove and 1 small-diced leek to the white mirepoix mix.Feel free to use whole butter or ghee if clarified is not available.If you are wanting to make cream of chicken soup or sauce, simply whisk in ¼ to 1/3 cup of heavy whipping cream once the original velouté is finished.