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1
In a small saucepan, cover the shrimp shells with the water and bring to a boil.
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2
Simmer for 20 minutes, then strain the shrimp stock into a bowl.
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3
Meanwhile, in a large skillet, heat the olive oil.
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4
Add the shrimp, garlic, onion and cayenne and cook over high heat until the shrimp begin to turn pink, about 3 minutes.
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5
Add the brandy and boil until reduced by half, about 2 minutes.
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6
Add the chopped basil and the sherry and simmer until the shrimp are just cooked through, about 2 minutes.
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7
Transfer the shrimp to a food processor, add the shrimp stock and puree until smooth.
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8
In a medium saucepan, melt the butter over moderate heat.
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9
Whisk in the flour and cook, whisking, until smooth, about 1 minute.
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10
Slowly whisk in the half-and-half and cook, whisking, until the roux is very thick, about 2 minutes.
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11
In a soup pot, combine the fish stock with the tomato paste and the shrimp puree and bring to a simmer over high heat.
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12
Slowly whisk in the roux and the heavy cream.
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13
Reduce the heat to moderately low and simmer until thick and creamy, about 20 minutes.
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14
Add the lemon juice and season with salt and pepper.
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15
Ladle the bisque into bowls, garnish with the sliced basil and serve.