In a medium sized pot, cook rice according to package directions.
While the rice cooks, chop carrots, celery and onion. In a separate large pot, melt butter and add vegetables and seasonings. Saute over medium heat for 10 minutes, until celery and onions are soft, then add broth. Simmer for about 20-30 minutes, until the rice is finished cooking.
Once rice is done, add it to the vegetable mixture along with the cream and simmer for another 5 minutes, stirring occasionally.
Serve hot and store for up to a week in the refirdgerator.