Peel and grate in long thin shreds, the carrots and add finely diced celery. Melt butter in saucepan and add the vegetables. Stir. Cover and simmer over very low heat for 20 minutes, without browning the vegetables. Add milk (or use 1/2 milk, 1/2 cream); bring to a boil. Heat oysters in enameled cast iron pan over medium heat; do not boil. Pour into milk and serve. Use salt and pepper to taste.
The soup should be served as soon as ready, otherwise it tend to curdle. The milk and vegetables can be prepared ahead of time and the oysters heated and served at the last minute.
To quote Mme. Benoit, "This traditional Quebec dish is still very much alive. My grandmother's recipe is, as far as I am concerned, the best there is. " Note: from Anne - it seems as oysters were used at Christmas. My maternal grandmother from the American midwest had a similar Christmas oyster dish although hers included corn.
Source: _My Grandmother's Kitchen" by Mme. Benoit