Finely mince the mushrooms, shallots, and garlic, then sauté in a dry pan over medium heat with fresh thyme until all moisture has evaporated.
Season the beef tenderloin with sea salt and black pepper on all sides.
Heat olive oil in a heavy skillet over high heat and sear the beef for 60 seconds per side until a brown crust forms, then remove and brush with Dijon mustard.
Lay a sheet of plastic wrap on a clean surface and arrange the prosciutto slices in a slightly overlapping rectangle.
Spread the mushroom duxelles evenly over the prosciutto, then place the seared beef in the center.
Use the plastic wrap to roll the prosciutto and mushrooms tightly around the beef, twisting the ends to form a tight log, and chill in the freezer for 15 minutes.
Roll out the puff pastry on a lightly floured surface, unwrap the chilled beef log, and place it in the center of the pastry.
Fold the pastry over the beef to seal it completely, trimming any excess, and place seam-side down on a parchment-lined baking sheet.
Brush the exterior of the pastry with the beaten egg yolk and bake at 425°F for 15 to 20 minutes until the crust is golden brown.
Remove from the oven and let the Wellington rest for 10 minutes before slicing to ensure the juices remain in the meat.