Melt the butter in a large saucepan over medium heat, and cook and stir the onion until golden, about 8 minutes. Stir in the flour until smooth, and cook and stir the mixture until it turns a pale golden color, about 5 minutes. Whisk in the chicken broth, stirring constantly to avoid lumps, then mix in the half-and-half, salt, crawfish tails, Worcestershire sauce, and cayenne pepper.
Reduce heat to medium-low, and continue whisking as soup comes to a simmer. Allow the bisque to simmer for about 5 minutes, until slightly thickened. Do not boil.
