For the mushroom mixture: In the bowl of a food processor, in two batches, pulse the mushrooms and shallots, until finely chopped, 12 to 15 times, stopping occasionally to scrape the sides of the bowl. Heat the olive oil in a large skillet over medium heat. Add the mushroom mixture. Cook, stirring often, until tender, beginning to brown and any moisture in the skillet has evaporated, 25 to 30 minutes. Add the garlic, thyme, salt and pepper. Cook, stirring often, for 1 minute. Stir in the parsley and remove from the heat. Let cool to room temperature, at least 30 minutes. For the Beef Wellington: Sprinkle the beef tenderloin all over with salt and pepper. In a large skillet over medium-high, heat the oil. Cook the beef tenderloin, turning occasionally, until browned on all sides, 10 to 12 minutes total. Remove the tenderloin from the skillet and set aside to cool for 30 minutes. Remove and discard the twine. On a clean work surface, overlap 2-3 pieces of plastic wrap to form a 22 x 18-inch rectangle. Lay the prosciutto slices on the plastic wrap, slightly overlapping each slice to form a 13 x 10 -inch rectangle in the center of the plastic wrap. Spread the cooled mushroom mixture evenly over the prosciutto. Rub the beef tenderloin all over with mustard and arrange lengthwise along the bottom third of the prosciutto rectangle. Using the plastic wrap as a guide, roll the beef tenderloin in the mushroom covered prosciutto to form a log. Wrap tightly in plastic wrap and chill at least 1 hour or up to 4 hours. Preheat the oven to 425°F. On a lightly floured surface, slightly overlap the 2 sheets of puff pastry and roll into a 15x12 -inch rectangle. Lightly brush the top third of a long side of the pastry with egg. Remove the plastic wrap from the beef tenderloin log and place the log lengthwise in the center of the puff pastry. Fold to completely seal the log in pastry, brushing any folds with egg to help them stick together and seal. Place the pastry wrapped tenderloin, seam side down, on a parchment-lined rimmed baking sheet. Brush the log lightly with the remaining egg. Using a small knife, cut 3 (1-inch) slits in the puff pastry to allow steam to escape.  Bake the Beef Wellington until the puff pastry is golden brown and a meat thermometer inserted in the center registers 120°F for medium-rare, 40 to 50 minutes, tenting with foil to prevent excess browning if needed. Remove from the oven and let rest at room temperature for about 15 minutes before serving.