Set a fine mesh sieve over a small bowl and pour the oysters over the sieve. This will remove any sand or grit from the liquor. Discard solids and save liquor.
In a medium saucepan, melt the butter over medium heat. Add the shallots and celery, stirring for 2-3 minutes until vegetables are slightly softened and translucent.
Turn the heat down to medium low and add the strained oyster liquor, milk, cream, thyme, salt and pepper. Heat slowly until broth reaches a simmer (just a few bub- bles rimming the pan) Do not boil, to avoid curdling the milk.
Slip the oysters into the broth and let them simmer for 2-3 minutes, just until the edges start to curl. You want the oysters to be tender, not tough – overcooking will make them rubbery.