Preheat your oven to 425°F (220°C).
Season the beef tenderloin with sea salt and black pepper on all sides.
Heat olive oil in a skillet over high heat and sear the beef for 1-2 minutes per side until browned but raw in the center; remove and brush with Dijon mustard while warm.
In the same skillet, sauté finely minced mushrooms, shallots, and thyme until all moisture has evaporated and the mixture forms a thick paste (duxelles).
Lay a piece of plastic wrap on a flat surface and arrange the prosciutto slices in an overlapping rectangle.
Spread the mushroom duxelles evenly over the prosciutto, then place the beef in the center and roll tightly using the plastic wrap; chill in the freezer for 10 minutes.
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, sealing the edges with a bit of beaten egg, and place seam-side down on a parchment-lined baking sheet.
Brush the entire pastry with the remaining beaten egg and bake for 15-20 minutes until the crust is golden brown and the internal beef temperature reaches 125°F for medium-rare.
Allow the Wellington to rest for 5-10 minutes before slicing into thick rounds.