Trim and discard tough or discolored stem ends and any bruised spots from mushrooms. Rinse common mushrooms and drain well. (If using chanterelles, submerge in cool water and gently agitate with your hands to loosen dirt. Drain, rinse under running water, and gently pat dry with a towel.) Coarsely chop mushrooms.
In a 5- to 6-quart pan over high heat, stir bacon until fat begins to render, about 1 minute. Add onion, celery, and garlic; stir until onion is limp, about 3 minutes. Add mushrooms and stir often until their liquid is evaporated and mushrooms begin to brown, 15 to 20 minutes.
Add cognac and stir to scrape up browned bits from pan bottom and sides. Add wine and boil until most of the liquid has evaporated, 1 to 2 minutes. Add broth and return to a boil, then cover, reduce heat, and simmer, stirring occasionally, to blend flavors, 20 to 30 minutes. Remove from heat.
In a blender, holding down lid with a towel, whirl mixture, a portion at a time, until smooth. Pour into a bowl. Stir in cream, then salt and pepper to taste. Chill, stirring occasionally, until soup is at room temperature, 10 to 15 minutes.
Spoon soup into six round soufflé dishes or ovenproof bowls (1 1/4- to 1 1/2-cup size; 3 1/2 to 4 1/2 in. wide) to within 1/2 inch of rim.
On a lightly floured board, roll each puff pastry shell into a round 1 to 1 1/2 inches wider than top of soufflé dishes. Brush egg in a 1/2-inch border around the bottom edge (unscored side) of each pastry round. Carefully drape each round, egg side down, over a dish so that it doesn't touch soup; press edges firmly around sides of dish. Brush more egg lightly over pastry tops and sides (discard remaining egg or save foranother use). Set dishes at least 1 inch apart in a 12- by 17-inch baking pan.
Bake in a 375° regular or convection oven until pastry is richly browned, 15 to 20 minutes. Serve at once, with sherry-shallot butter to stir into portions at the table.
Sherry-shallot butter: In an 8- to 10-inch frying pan over high heat, stir 1/3 cup minced shallots and 1/3 cup dry sherry often until liquid is evaporated and shallots begin to brown, 5 to 8 minutes. Pour into a small bowl and let cool. Add 3 tablespoons butter (at room temperature) to shallots and mix. Divide into six equal portions and, with your hands, roll each into a ball. Arrange on a small plate. Cover and chill until firm, at least 15 minutes.