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1
Melt butter in a large stockpot over medium-high heat.
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2
Saute shallots until golden, about 3 minutes.
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3
Add mushrooms and cook over high heat until slightly browned, about 2 additional minutes.
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4
Remove from heat and add brandy and Madeira reserving 1/4 cup of each for final seasoning.
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5
Cook over high heat until liquid is reduced by half.
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6
Add lobster stock and return to a boil.
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7
Reduce to a simmer and cook, uncovered, 15 to 30 minutes, depending on the strength of your stock.
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8
(Weaker stocks need to cook longer to concentrate their flavors.)
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9
Occasionally skim and discard foam that rises to the top.
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10
Make beurre manie by mixing butter and flour with your fingers to form a smooth paste.
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11
Press onto ends of a whisk.
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12
When broth has a strong, almost salty, lobster flavor, add cream and bring it back to a boil, skimming foam occasionally.
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13
Then whisk in beurre manie until dissolved.
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14
Cook an additional 5 minutes over high heat, whisking occasionally.
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15
Strain through a fine sieve, pressing with the back of a ladle to extract all juices.
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16
Season with lemon juice, reserved brandy and Madeira, and hot pepper sauce, and serve immediately.
