Finely mince the mushrooms, shallots, and garlic until they reach a paste-like consistency.
Sauté the mushroom mixture in olive oil over medium heat until all moisture has evaporated and the mixture is browned; stir in fresh thyme and cool completely.
Season the beef tenderloin with sea salt and black pepper, then sear in a hot pan for 1-2 minutes per side until browned but raw in the center.
Brush the seared beef with Dijon mustard while still warm to allow the flavors to penetrate.
Lay a piece of plastic wrap on the counter, place the prosciutto slice on top, spread the mushroom duxelles 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 fridge for 15 minutes to set the shape.
Roll out the puff pastry between two sheets of parchment paper, unwrap the chilled 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 wash, and trim any excess dough for a clean finish.
Place the Wellington on a parchment-lined baking sheet, brush the top with the remaining beaten egg, and bake at 400°F for 20-25 minutes until the pastry is golden brown.