Place a large pot on the stove over medium heat, and heat the butter in this until it is melted. Toss in the onion and cook it, stirring it with a wooden spoon until it becomes soft and translucent.
Next, pour in your chicken broth, and bring the liquid up to a boil. Add the garlic, cayenne pepper, bay leaves, Cajun seasoning, salt, and pepper into the boiling broth. Stir in the corn, and once you’ve added everything, reduce the heat. Simmer this mixture on medium-low heat for around 10 minutes.
Take one cup of soup out of the pot, and set it aside to cool. Once it stops steaming, pour it into a food processor, along with the Half-and-Half. Blitz it in the processor until it forms a puree, and put this aside to use later.
Then, mix the milk and flour together in a small bowl. Gradually drizzle this into the pot of simmering soup, stirring constantly all the while. Allow the soup to simmer once again, for a minute or two, and then stir in the puree of broth and Half-and-Half.
Bring the heat down to low, and add in the crab meat. Stir it in gently and cook it until the bisque is warmed through. Ladle it into low two-handled cups placed on saucers – the traditional method for serving bisque – and enjoy.