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1
Simmer white mushrooms, onions, water, and 1 tsp salt in a 6-qt stockpot, uncovered, 1 1/2 hours.
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2
Strain mushroom mixture through a large sieve lined with a damp paper towel into a large saucepan, pressing gently on solids to extract as much liquid as possible. Mushroom mixture should yield about 4 cups consomme. (If less, add water; if too much, boil consomme until it is reduced to 4 cups.) Discard solids. Season consomme with salt and pepper.
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3
Pour boiling water over morels in a small bowl and soak until morels are softened, about 20 minutes.
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4
Transfer morels with a slotted spoon to a medium-mesh sieve set over a bowl. Press on morels with back of spoon to remove liquid, then add liquid from morels to soaking liquid and reserve.
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5
Rinse morels to remove any grit, then transfer to a small saucepan and add Madeira. Simmer, covered, 5 minutes.
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6
Add morels and Madeira to consomme in saucepan. Let reserved soaking liquid settle, then slowly pour into consomme, being careful to leave last tablespoon (containing sediment) in bowl.
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7
Add chives to consomme and simmer, covered, 3 minutes, then chill, uncovered, until cold, about 1 hour.
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8
If pastry comes as 1 sheet, cut crosswise in half. Roll out each piece of pastry into a 13-inch square on a lightly floured surface with a lightly floured rolling pin. Chill on baking sheets until firm, about 1 hour.
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9
Cut out 3 rounds from each sheet of puff pastry using template. Brush any excess flour from both sides of pastry rounds. Brush tops with some of beaten egg. Chill pastry rounds on baking sheets until firm, about 1 hour.
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10
Preheat oven to 425u00b0F with rack in middle.
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11
Divide cold soup among bowls. (Do not chill soup in bowls.) Lightly beat yolk, then brush around edge and down side of each bowl (a 1/2-inch-wide strip). Working quickly, place each pastry round over a bowl and pull slightly so pastry is taut. Press edge down against side of bowl to seal tightly.
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12
When all bowls are covered with pastry, arrange in a large 4-sided sheet pan and bake until pastry is puffed and golden brown, 15 to 20 minutes. Serve immediately.
