Using butcher's twine, tie the tenderloin at 1-inch intervals. Trim ends of the twine. Season liberally with Kosher salt and freshly ground black pepper.

Heat 2 tablespoons of oil in a 12-inch cast iron or stainless steel skillet over high heat until smoking. Add the tenderloin and cook without moving until well-browned on the first side, about 2 minutes. Rotate tenderloin and continue cooking until browned on all sides, about 10 minutes total. Transfer to a large plate. Set the skillet aside.

Combine the horseradish, mustard, and 1 teaspoon black pepper in a small bowl. When the tenderloin is cool enough to handle, cut off and discard twine, then rub on all surfaces with horseradish/mustard mixture. Place in the refrigerator, uncovered.

Place half the mushrooms in the bowl of a food processor and pulse until very finely chopped, scraping down sides and redistributing the mushrooms with spatula as necessary, about 10 short pulses. Transfer to a bowl. Repeat with the remaining mushrooms.

Add the brandy. Scrape the bottom of the skillet with a wooden spoon to release any browned bits. Continue to cook until the brandy is nearly dry, about 4 minutes.

Add the 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. (See Notes.)

Lay a double layer of plastic wrap about 2 feet long and 1 foot wide on the counter. Lay phyllo dough on top of plastic wrap. Shingle the prosciutto on top of phyllo to create a thin, even, overlapping layer, leaving a 2-inch border along the bottom and top of the phyllo dough. Spread the mushroom mixture evenly over the prosciutto layer.

Place the tenderloin along the very bottom edge of the prosciutto/mushroom layer. Spread the pâté on top of tenderloin. Carefully roll the tenderloin on the mushroom, prosciutto and phyllo (it’s okay if this cracks a bit), using the plastic wrap to help tighten it as you roll. Once the beef is completely rolled up, re-wrap with more plastic wrap, twisting the ends to make sure the roll is very tight. Return to the refrigerator for at least 30 minutes.

Dust the countertop lightly with flour. Spread the puff pastry on the counter and, using a rolling pin, roll it into a rectangle at least 4 inches wider than the beef roll on its shorter side.

Unwrap beef roll and place it along the very bottom edge of puff pastry with the pâté side facing up. Brush 6 inches of the puff pastry just above the beef roll with the beaten egg (save the remaining egg for the top of the pastry). Carefully roll the beef in the puff pastry until it is completely wrapped. You should end up with the pâté-side facing up again (if you can’t tell, don’t worry), with the puff pastry seam meeting on the bottom. Trim pastry with a sharp knife.

Fold sides of the puff pastry protruding from either end of the beef roll towards the center, then fold the top flaps down. Trim off the bottom flaps carefully. (It’s kind of like wrapping a present.)

Roll the entire beef roll over so that the bottom is facing up, then 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. (See Notes).

Transfer the Beef Wellington to a parchment-lined baking sheet and brush all over with remaining beaten egg.

Use a sharp paring knife to lightly score (do not cut all the way through) a decorative pattern in the pastry.

Sprinkle liberally with flaky or coarse salt.

Bake until pastry is golden brown (and puffed) and center of roast registers 110°F for rare or 120°F for medium-rare on an instant-read thermometer, 35 to 45 minutes. Remove it from the oven and allow it to rest for 10 minutes.

Use a thin metal spatula to loosen Wellington from parchment paper, then carefully transfer it to a carving board. Slice off the ends with a sharp knife. Carve the Beef Wellington and serve.