Finely mince the cremini mushrooms, garlic, and fresh thyme, then sauté in a dry pan over medium heat until all moisture evaporates and they form a thick, concentrated paste.
Season the beef tenderloin with sea salt and black pepper, then sear in a hot pan with ghee for 1 minute per side until a crust forms, keeping the center raw.
Remove the beef from the pan and immediately brush all sides with Dijon mustard while warm, then set aside to rest.
Lay a sheet of plastic wrap on a flat surface and arrange the prosciutto slices in a slight overlap to form a rectangle.
Spread the mushroom duxelles evenly over the prosciutto, then place the beef in the center and roll tightly using the plastic wrap to form a log.
Chill the beef log in the refrigerator for 15 minutes to firm up the shape.
Roll out the puff pastry on a lightly floured surface, unwrap the beef, and place it in the center of the pastry.
Fold the pastry over the beef, trimming any excess to avoid a thick base, and seal the edges using a small amount of the beaten egg yolk.
Place the Wellington seam-side down on a parchment-lined tray, brush the entire exterior with the remaining egg yolk, and bake at 425°F for 15-20 minutes until the pastry is golden brown and the beef reaches 125°F for medium-rare.