Strain the oyster water into a saucepan. Bring to a simmer and cook for about five minutes.
While that's going on, chop all the vegetables and the anchovies in a food processor into a rough puree. Add a little water to keep everything moving if necessary.
In a small saucepan, melt the butter over medium-low heat and add the flour. Stir to make a blond roux. Add the pureed vegetables to the roux, and continue to stir for about a minute. Add the Herbsaint or Pernod and cook for about another minute.
Add the vegetable mixture to the oyster water. Add the salt, cayenne, white pepper, Worcestershire, bitters, and thyme to the soup. Simmer for five minutes.
Just before serving, add the oysters and all the water they were packed in (strained). Cook until the oysters are curly at the edges. Stir, check seasonings and add salt and cayenne to taste.
