Preheat oven to 425°F and line a baking sheet with parchment paper.
Season the beef tenderloin with sea salt and black pepper on all sides.
Heat ghee in a cast-iron skillet over high heat and sear the beef for 1 minute per side until browned but raw in the center, then remove and brush with Dijon mustard.
In the same skillet, sauté finely chopped mushrooms, minced shallot, garlic, and thyme until all moisture has evaporated and the mixture forms a thick paste.
Lay a piece of plastic wrap on the counter, place the prosciutto slice on top, spread the mushroom mixture over the prosciutto, and place the beef in the center.
Roll the prosciutto and mushrooms tightly around the beef using the plastic wrap and chill in the freezer for 10 minutes to firm up.
Roll out the puff pastry on a lightly floured surface, place the beef bundle in the center, and wrap the pastry around it, sealing the edges with a bit of egg wash.
Place the Wellington on the baking sheet, brush the entire exterior with the remaining beaten egg wash, and score the top lightly with a knife.
Bake for 15 to 20 minutes until the pastry is deep golden brown and the internal temperature of the beef reaches 125°F for medium-rare.
Allow the beef to rest for 10 minutes before slicing into thick rounds.