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In a large soup pot melt butter over medium heat. Sauté carrots, celery, onion, leek, fennel, peppercorns and bay leaves for 3-4 minutes.
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Deglaze pan with cooking sherry and add lobster body and shells. Stir and bring to a light simmer, about 2 minutes.
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Reduce heat to low, once sherry stops simmering, stir in milk and season with paprika and cayenne. Cover and steep for 1 hour, stirring frequently.
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Strain broth using a fine mesh strainer and discard vegetables, whole spices and shells. Return broth to the stove, stir in cream and season to taste with salt.
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To serve ladle hot broth into bowls and fill with reserved lobster meat. Garnish with fresh chives before serving.