Remove the beef from the refrigerator about an hour ahead so it has time to lose its chill.
Pat the beef dry and season all over with salt and pepper. Heat the oil in a 12-inch skillet over high heat until very hot. Sear the beef until it is evenly browned all over (don't worry about the ends), 2 to 3 minutes per side. Transfer the beef to a baking sheet and let cool.
In a medium bowl, mash the pâtè and the duxelles with a fork until they form a soft paste.
Lay 4 crêpes on a clean work surface, overlapping them just enough to give you a 13x13-inch roughly square surface. Dot the pâtè mixture over the crêpes, then use an offset spatula, or a knife, to spread it evenly across the crêpes' surface.
Place the tenderloin in the center of the crêpes and carefully wrap them around the filet, pressing and molding them into place. Trim off any excess crêpe at the ends.
Fuse the two puff pastry sheets together by slightly overlapping them and lightly rolling over the seam until adhered. On a lightly floured surface, roll out the puff pastry to a 13x16-inch rectangle.
Transfer the wrapped beef to the center of the pastry and tuck any crêpes that have come loose back into place. Bring the pastry up around the beef, smoothing out any air pockets.
Brush some of the beaten egg along the bottom edge of the seam and then press gently to seal; trim off any excess puff pastry. Seal the pastry similarly at the ends.
Lightly grease a large baking sheet with the butter. Lift the Wellington onto the sheet, seam side down. Refrigerate for at 15 minutes and up to 3 hours. (If refrigerating longer than 1 hour, let the Wellington sit at room temperature for 1 hour before baking.)
At least 20 minutes before baking, position a rack in the center of the oven and heat the oven to 425 F.
Brush the Wellington with the remaining beaten egg. Using a sharp knife, score the surface of the pastry with 3 diagonal lines: IMPORTANT: Be careful not to cut all the way through the pastry.
Put the Wellington in the oven and immediately reduce the temperature to 425 F. Roast for 10 minutes, then reduce the heat to 400 F and roast until an instant-read thermometer inserted into the center of the Wellington registers 135 F for medium-rare, 20 to 25 minutes. Transfer to a carving board and let the Wellington rest for 10 minutes. (The Wellington can rest up to 3 hours before cutting).
Meanwhile, finish the sauce by heating it in a 12-inch skillet over medium heat. When it begins to simmer, reduce the heat to low and whisk in the butter, a few pieces at a time. Do not allow it to boil. Season to taste with salt and pepper.
Thickly slice the Wellington and serve it with the sauce.