Cook the filet in a roasting pan in the middle of a preheated oven at 400 F for about 25 minutes. Let the filet cool completely. Remove the string carefully, so the tenderloin does not fall apart. Skim the fat from the pan juices and reserve the juices.
In a heavy skillet, cook the mushrooms in unsalted butter over medium-low heat, stirring continually. When the liquid has evaporated and the mixture is dry, season with salt and pepper and permit them to cool totally.
Spread the fillet evenly with the pate, covering the top and sides. Next, spread the mushrooms over the pate.
On a floured surface, roll the puff pastry into a rectangle of about 20 inches by 12 inches, or just large enough to enclose the fillet completely. Carefully invert the filet over the middle of the dough. Fold the long sides of the dough up and over the filet to enclose it. Brush the edges of the dough with egg white and pinch them together to seal. Fold the ends of the dough over the filet and seal them with the remaining egg white.
Spray a jelly-roll pan or shallow roasting pan with nonstick oil. Transfer the filet, seam side down, to the pan. Brush the dough with egg wash.
Roll out additional dough and cut shapes with decorative cutters. Arrange the cutouts on the dough-covered filet and brush them with remaining egg wash. Chill the filet for at least 1½ hours before cooking.
Bake for 30 minutes in the middle of a preheated oven at 400 F. Reduce the heat to 350 F and bake for another 5 or 10 minutes more. For medium-rare meat, the meat thermometer should register 130 F. Let the filet stand for about 15 minutes before serving.