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Rinse the dried mushrooms in cold water, put them into a small bowl and cover them with hot water. Let soak for 20 minutes.
Heat 2 tablespoons oil in a medium skillet over medium-high heat. When the pan is very hot, season the meat with salt and pepper and sear on each side for 1 minute per side. Set aside.
Turn the heat down to medium, add the shallots to the pan and cook until they are soft, 4 to 5 minutes. Add the butter and fresh mushrooms and cook for another 2 to 3 minutes. Drain the dried mushrooms and chop them finely. Add them to the pan along with the sherry, if using. Turn the heat up a bit and cook until the mushrooms are almost dry, 3 to 4 minutes. Add the thyme and season with salt and pepper. Cook for 1 more minute, take the pan off the heat and set aside.
Preheat the oven to 400 degrees F.
Remove the pastry from the refrigerator. Put a large tablespoon of the mushroom mixture in the center of a pastry square and spread it out to the same size as the meat. Place a piece of tenderloin on top and brush some egg wash around the edges of the pastry. Fold up the corners and sides of the pastry so they meet and overlap slightly in the middle. Turn it over so the seams are down and shape it into a neat package with your hands. Repeat with the other three squares. If the pastry has gotten soft, put the packages back in the refrigerator for 5 to 10 minutes to firm up. This will make sure the pastry does not just melt into a gooey mess in the oven before it has a chance to puff up. Save the remaining mushroom mixture for the sauce.
When you are ready to bake, cut a design into the top of each package with a paring knife. Brush them all over with egg wash. Bake for 14 minutes for medium rare or adjust the time shorter or longer according to how you like your meat cooked.
While the Wellingtons are baking, reheat the mushroom mixture. Add the cream and cook on high for 2 minutes. Taste and adjust the seasoning. Remove from the heat, cover and keep warm.
When the Wellingtons are ready, remove them from the oven and serve with the sauce and a big glass of hearty red wine.