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1
Plunge lobsters headfirst into an 8-quart pot of boiling salted water*.
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2
Loosely cover pot and cook lobsters over moderately high heat 9 minutes from time they enter water, then transfer with tongs to sink to cool.
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3
When lobsters are cool enough to handle, twist off claws and crack them, then remove meat.
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4
Halve lobsters lengthwise with kitchen shears, beginning from tail end, then remove tail meat, reserving shells.
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5
Cut all lobster meat into 1/4-inch pieces.
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6
Discard any remaining lobster innards, then rinse and dry shells.
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7
Heat butter in a 2-quart heavy saucepan over moderate heat until foam subsides, then cook mushrooms, stirring, until liquid that mushrooms give off is evaporated and they begin to brown, about 5 minutes.
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8
Add lobster meat, paprika, salt, and pepper and reduce heat to low.
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9
Cook, shaking pan gently, 1 minute.
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10
Add 1 tablespoon Sherry and 1/2 cup hot cream and simmer 5 minutes.
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11
Whisk together yolks and remaining tablespoon Sherry in a small bowl.
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12
Slowly pour remaining 1/2 cup hot cream into yolks, whisking constantly, and transfer to a small heavy saucepan.
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13
Cook custard over very low heat, whisking constantly, until it is slightly thickened and registers 160F on an instant-read thermometer.
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14
Add custard to lobster mixture, stirring gently.
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15
Preheat broiler.
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16
Arrange lobster shells, cut sides up, in a shallow baking pan and spoon lobster with some of sauce into shells.
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17
Broil lobsters 6 inches from heat until golden brown, 4 to 5 minutes.
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18
Serve remaining sauce on the side.
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19
When salting water for cooking, use 1 tablespoon salt for every 4 quarts water.
