1. Thaw puff pastry. Set butter out to soften. Line baking sheet with foil.
2. Melt 1 tablespoon butter in large sauté pan on medium-high. Coat tenderloin with salt and pepper (wash hands); add to pan and cook 4 minutes, turning occasionally, or until browned all over. Reduce heat to medium-low and cook 25 minutes, turning occasionally, or until 120°F. Remove from pan and set aside.
3. Place mushrooms and onions in food processor bowl (or blender) and pulse until finely chopped. Melt remaining 2 tablespoons butter in same pan. Add mushroom mixture and cook 15–20 minutes, stirring occasionally, until mushrooms are dry. Remove from pan and let stand to cool slightly.
4. Preheat oven to 425°F. Coat work surface with flour. Roll out puff pastry sheet into rectangle 4 inches longer and 6 inches wider than tenderloin. Spread mushroom mixture evenly on pastry sheet , leaving a 1-inch border. Place tenderloin in center of mushroom mixture; fold pastry over tenderloin, press to seal, and place seam-side down on baking sheet. Tuck ends under to seal. Brush pastry with egg.
5. Bake 25–30 minutes until pastry is golden and beef is 125°F (for medium rare; warm red center), 130°F (for medium; warm pink center), or up to 170°F (for well done). Transfer to cutting board and let stand 10 minutes before slicing; temperature will rise 5–10°F during this time. Slice and serve.

Chef's Tip: Cut out decorative pieces of dough from remaining puff pastry and place on top of wellington before baking if desired.