Make mushroom consomme: In a 6-quart stockpot or kettle, combine consomme ingredients and simmer, uncovered, 2 hours. Pour consomme through a large fine sieve lined with a rinsed and squeezed paper towel into a large saucepan, pressing gently on solids, to yield about 5 cups consomme (if yield is not enough, add water to make 5 cups; if too much, boil consomme until reduced to 5 cups.) Season consomme with salt and pepper.
Prepare morels while consomme is simmering: In a small bowl pour boiling water over morels and let stand 20 minutes, or until morels are soft. Remove morels, reserving soaking liquid, and in a small saucepan simmer morels in Madeira, covered, 5 minutes. Add morel mixture to consomme. Let reserved soaking liquid settle and slowly pour it into consomme, being careful to leave last tablespoon (containing sediment) in bowl. Simmer consomme, covered, 3 minutes and cool to room temperature. Consomme can be made 2 days ahead and chilled, covered. Bring consomme to room temperature before proceeding.
Have ready 6 (12-ounce) "truffle soup bowls" or 9 to 10-ounce ovenproof ramekins, each measuring 3 1/2 to 4-inches across top. Divide consomme, including morels, and chives among bowls or ramekins.
Prepare pastry "hats": On a lightly floured surface roll out 1 sheet puff pastry into a 12-inch square. With a round cutter at least 3/4 inch larger than diameter of bowls cut out 4 rounds. Roll out second puff pastry sheet and cut out 2 more rounds in same manner. Brush any excess flour from both sides of rounds.
Working with 1 pastry round at a time, brush a 1/2-inch-wide border of egg wash around pastry edges and invert pastry rounds over bowl or ramekins, carefully stretching 1/2-inch down side and pressing to seal.
When all bowls or ramekins are covered with pastry, brush tops with remaining egg wash. Pastry covered consomme may be prepared up to this point 4 hours ahead and chilled. Preheat oven to 400 degrees F. Arrange bowl or ramekins on a large baking sheet and bake consomme in middle of oven until pastry "hats" are puffed and golden, 12 to 18 minutes.
*available at specialty foods shops and by mail order.