Melt butter in a large stockpot over medium heat. Stir in flour to make a smooth paste. Cook, stirring for about 3 minutes. Add onion, celery, and garlic. Season with salt and pepper. Continue to cook, stirring for about 4 minutes.

Gradually whisk in half-and-half so that no lumps form. Stir in heavy cream and chicken broth. Bring to a simmer. Add 1/4 cup sherry. Season with dill, Worcestershire sauce, and hot sauce. Cover and simmer until soup has reduced by 1/3, about 30 minutes. Add crabmeat and simmer for 10 more minutes.

Ladle soup into bowls. Top each serving with a splash of remaining 1/4 cup sherry and garnish with chives.