Sweet, spicy notes of cinnamon and star anise permeate the broth for this delicious crawfish stew that gets thickened at the end with a cold, dark roux for the perfect consistency. If you want to turn up the heat level, feel free to add Tabasco to your heart's desire.
Bring a large pot of water to a boil. Blanch the crawfish until cooked through, remove from the pot, and let cool. Reserve the cooking liquid.
Separate the crawfish tails from the bodies. Remove the meat from the shells and set aside. Place the shells and bodies back in the water, add the bay leaves, black peppercorns, and red-wine vinegar. Simmer for 1 ½ hours. Strain through a fine sieve and reserve the cooking liquid.
In a pot, melt the butter over low heat. Sweat the onions, carrots, and celery until softened. Add the white wine and bring to a simmer. Strain through a cheesecloth and reserve the wine. Add the onions, carrots, celery, thyme, rosemary, cinnamon sticks, and star anise to the cheesecloth. Tie off with some cooking twine and place at bottom of an 8-quart earthenware container.
Add the wine, crawfish cooking liquid, tomato paste, and canned tomatoes. Simmer until reduced by approximately 1/3, about 2 hours. Purée the mixture in a blender and strain. Add back to the earthenware container.
Place the crawfish tails back in the liquid and stir the cold roux into the hot liquid to create the proper consistency. Season with the lime juice, sugar, salt, and white pepper, to taste. Add more red-wine vinegar and some Tabasco, if desired. Garnish with chopped fresh herbs, if using.