Heat a small sauté pan until very hot and quickly sear foie gras until browned on both sides. Transfer foie gras to paper towels to drain and set aside. Reserve the rendered foie gras fat.
Transfer 3 tablespoons of the rendered foie gras fat to a large sauté pan along with the butter. Heat over medium-high heat and sauté the shallots for 2 minutes. Add the garlic and sauté for 1 minute. Add the mushrooms, salt and pepper, and sauté, stirring frequently, until the mushrooms give off their liquid. Continue to cook until almost all of the liquid has evaporated, about 7 minutes. Deglaze the pan with the Madeira and cook until all liquid has evaporated, about 2 minutes. Transfer to a small bowl and set aside to cool to room temperature.
On a lightly floured surface, roll out puff pastry sheets to a thickness of 1/8-inch. Cut into 12 2-inch rounds and 12 3 1/2-inch rounds. Divide duxelles between the 12 2-inch rounds and top each mound of duxelles with 4 snails. Cut reserved foie gras into 12 pieces and place one piece on top of each mound of snails and duxelles. Using a pastry brush or your fingers, brush the edges of each 2-inch round with some of the beaten egg, then top each 2-inch round with one of the larger rounds, easing to cover snails so that the edges line up. Crimp edges closed with your fingers or with the tines of a fork and make a small slit in the top of each dome with the tip of a paring knife. Brush each dome with a little of the beaten egg, transfer domes to an ungreased baking sheet and chill thoroughly.
Preheat oven to 400ºF and bake the domes for 12 to 15 minutes, or until golden brown and puffed. Serve immediately, napped with some of the sauce.
While domes are baking, make the sauce by melting the reserved foie gras fat and butter and sauté shallots until soft, about 2 minutes. Add garlic and fresh thyme and cook for 1 minute. Add chicken stock and cook until liquid has reduced to a quarter of its original volume. Add heavy cream and cook until sauce is thick and coats the back of a spoon.
Season to taste with salt and freshly ground black pepper and serve with the hot escargot domes.
Yield: 12 domes, serving 6 as a first course