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Step 1
Using butcher's twine, tie tenderloin at 1-inch intervals. Trim ends of twine. Season liberally with salt and pepper.
Step 2
Heat 2 tablespoons oil in a cast iron or stainless steel skillet over high heat until smoking. Add tenderloin and cook without moving until well-browned on first side, about 2 minutes. Rotate tenderloin and continue cooking until browned on all sides, about 10 minutes total. Transfer to a large plate.
Step 3
Combine horseradish, mustard, and 1 teaspoon black pepper in a small bowl. When tenderloin is cool enough to handle, cut off and discard twine, then rub on all surfaces with horseradish/mustard mixture. Place in refrigerator, uncovered.
Step 4
Place half the mushrooms in the bowl of a food processor and pules until very finely chopped, scraping down sides and redistributing mushrooms with spatula as necessary, about 10 short pulses. Transfer to a bowl. Repeat with remaining mushrooms.
Step 5
Heat butter in a 12-inch skillet over medium-high heat until melted. Add mushrooms and cook, stirring occasionally, until mushrooms have exuded all their liquid and start to sizzle, about 8 minutes. Continue cooking until mushrooms begin to brown and leave browned bits stuck to bottom of pan, about 4 minutes longer. Add shallots and thyme and cook, stirring frequently, until softened, about 2 minutes.
Step 6
Add brandy. Scrape bottom of skillet with a silicone spatula or wooden spoon to release browned bits. Continue to cook until brandy is nearly dry, about 4 minutes. Add heavy cream and soy sauce and continue to cook, stirring frequently until mixture is thick and collects in one large mass when you shake the skillet. Season to taste with salt and pepper. Transfer to a bowl and place in the refrigerator.
Step 7
Season foie gras liberally with salt and pepper. Heat remaining half teaspoon oil in a a small cast iron or stainless steel skillet over high heat until smoking. Add foie gras and cook without moving until well browned on first side, about 30 seconds. Carefully flip with a small offset spatula and brown second side, about 30 seconds longer. Transfer foie gras to a paper towel-lined plate. Pour rendered fat into mushroom mixture, stir to combine, and return to refrigerator. Use a sharp knife to split each piece of cooked foie gras in half horizontally. Transfer to a plate and place in refrigerator. Allow all ingredients to chill for at least 30 minutes.
Step 8
Lay a double layer of plastic wrap about 2 feet long and 1 food wide on your cutting board. Lay fillo dough on top of plastic wrap. Shingle prosciutto on top of fillo to create a thin, even, overlapping layer, leaving a 2-inch border along the bottom and top of the fillo dough. Spread mushroom mixture evenly over ham layer.
Step 9
Place tenderloin along the very bottom edge of the ham/mushroom layer. Spread sliced foie gras evenly over top of tenderloin (see note). Carefully roll tenderloin in mushroom, hamd, and filo, using the plastic wrap to help tighten it as you roll. Once beef is completely rolled up, re-wrap with more plastic wrap, twisting the ends to make sure roll is very tight. Return to refrigerator.
Step 10
Dust board or countertop lightly with flour. Spread puff pastry on board and, using a rolling pin, roll it into a rectangle at least 4-inches wider than the beef roll on its shorter side.
Step 11
Unwrap beef roll and place along very bottom edge of puff pastry with the foie gras side facing up. Brush 6 inches of puff pastry just above beef roll with beaten egg. Carefully roll the beef in the puff pastry until it is completely wrapped. You should end up with the foie gras-side facing up again, with the puff pastry seam meeting on the bottom. Trim pastry with a sharp knife.
Step 12
Fold sides of puff pastry protruding from either end of the beef roll towards the center, then fold the top flaps down. Trimm off the bottom flaps carefully.
Step 13
Roll entire beef roll over so that the bottom is facing up, the fold up the end flaps to seal completely. Roll beef back right-side up. Transfer to a plate and chill for at least 30 minutes.
Step 14
Adjust oven rack to center position and preheat oven to 425°F (218°C). Transfer Wellington to a foil-lined baking sheet and brush all over with beaten egg. Use a sharp paring knife to score a decorative pattern in the pastry. Sprinkle liberally with coarse sea salt. Bake until pastry is golden brown and center of roast registers 110°F (43°C)for rare or 120°F (49°C) for medium-rare on an instant-read thermometer, 35 to 45 minutes. Remove from oven and allow to rest for ten minutes.
Step 15
Use a thin metal spatula to loosen Wellington from foil, then carefully transfer to a carving board. Slice off the ends with a sharp knife. Carve Wellington, sprinkle cut surfaces with chives and more coarse salt, and serve.