In a four to 5 quart heavy stock pot, heat the butter over medium high until melted and bubbling, then add the celery, carrots and onion. Sautee 5 minutes until softened.
Add the thyme, rosemary and chicken or turkey broth. Cover and bring to a simmer. Add half the salt, all of the pepper and the rice. Reduce heat to low and simmer covered until the rice your using is tender; check the box or bag for cooking times.
Once the rice is soft, add the vinegar. In a small cup add the cream and flour and stir to combine and remove any lumps. Add it to the main pot, then add the turkey or chicken and stir to combine. Bring to a gentle simmer over low heat again and simmer 5 minutes to thicken.
Taste for seasoning and add the last half of the salt if needed. This depends on how salty your broth was to begin with. Serve warm.