Bring beef tenderloin to room temperature. Tie tenderloin at 4-6 even intervals with kitchen twine to help keep it's shape. Season on all sides with kosher salt and pepper.
Drizzle a heavy bottomed skillet with olive oil. Seer the meat on high for 2 minutes on all sides including ends. The ends won't take as long. (If meat is thicker, 3 minutes per side)
Place onto a platter and into the fridge to cool for 1 hour. If preparing in advance, cover with plastic wrap only after the meat has cooled, to prevent it cooking further.
Meanwhile, add butter, mushrooms and onion to pan. Season with salt and black pepper to your taste. Cook for 20 minutes over medium heat. Add garlic, teriyaki and thyme, continue to cook until completely dry. set aside to cool.
On a non-stick floured surface, roll puff pastry into a rectangle roughly 4 inches longer and 6 inches wider than the tenderloin. Brush entire surface with beaten egg wash.
Spread from end to end with cooled mushrooms leaving a 1 inch border Remove kitchen twine from tenderloin.
Center tenderloin on mushrooms then fold pastry over ending seam side down. Tuck ends under or trim using extra pastry to decorate the top. Transfer to a large piece of plastic wrap, Wrap tightly and chill for 30 minutes.
To bake: Preheat oven to 400°F. Fit a rimmed baking sheet with an oven safe rack or line with parchment. Remove plastic wrap and center beef wellington on pan.
Brush on all sides with beaten egg wash. May decorate with additional puff pastry, if desired. Use a sharp knife to cut 3 or 4 slits on top.
Bake for 40 minutes or until internal temperature is 125-130°F for rare, 135-140°F for medium-rare and 140-145°F for medium.
Rest on pan for 10 minutes. Slice and serve with gravy, if desired.