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