Make the duxelles Heat the butter and oil in a 10-inch skillet over low heat. Add the shallots and cook, stirring often, until translucent, 3 to 4 minutes. Add the mushrooms, stir well, and raise the heat to medium. Cook, stirring occasionally, until the mushrooms have cooked down to a thick, almost black mixture, about 15 minutes. Season with a pinch of salt and a few grinds of pepper. Stir in the parsley; then transfer to a small bowl and cool completely. (The duxelles can be refrigerated for up to 2 days or frozen for up to 2 months.) Begin the Madeira sauce Bring 6 cups of the stock to a boil in a 12-inch skillet over medium-high heat and boil until reduced to 2 cups, 20 to 25 minutes. Add the Madeira and continue boiling until the liquid is again reduced to 2 cups, about 5 minutes. Season to taste with salt and pepper. (The sauce can be prepared to this point up to 1 day ahead. Finish the sauce just before serving the Wellington.) Make the crêpes In a large bowl, whisk the flour and salt. Make a well in the center, break in the eggs, and add 1/4 cup of the milk. Gently whisk the eggs and milk, gradually incorporating the flour. Slowly whisk in the remaining milk to make a smooth batter. (The batter can be covered and set aside for up to an hour at this point.) Melt the butter in a 10-inch skillet over medium-low heat. Swirl the pan to coat with the butter; pour the excess butter out into a small bowl. Whisk 1 Tbs. of the melted butter into the batter. Reserve the rest for greasing the pan between crêpes. Increase the heat to medium high and pour 1/4 cup of the batter into the skillet. Swirl so the batter thinly and evenly coats the base of the pan. Cook until the crêpe is spotted with brown on the underside, about 1 minute, then flip and cook the other side until lightly browned, 30 seconds to 1 minute more. Repeat with the remaining batter, greasing the pan off the heat as necessary. Transfer the crêpes to a plate, separating them with sheets of parchment, and cool. You’ll need 4 crêpes. Assemble and bake the Wellington 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 cool. In a medium bowl, mash the pâté 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 pâté mixture over the crêpes, then use an offset spatula 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. If using store-bought puff pastry that’s packaged as 2 sheets, fuse the 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 (for store-bought puff, roll in the direction of the seam). 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. 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 least 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 475°F. Brush the Wellington with the remaining beaten egg. Using a sharp knife, score the surface of the pastry with diagonal lines, being 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. Meanwhile, finish the sauce: Heat the sauce 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.
