Pat the beef tenderloin dry and season all over with salt and pepper
Sear the tenderloin in a hot pan with oil until browned on all sides
Brush the beef with Dijon mustard and let it cool
Finely chop mushrooms, shallots, and garlic
Cook the mushroom mixture in a pan until all moisture evaporates
Add thyme and cook until the mixture is dry and paste-like
Let the mushroom duxelles cool completely
Lay out plastic wrap and arrange prosciutto slices in an overlapping layer
Spread the mushroom mixture over the prosciutto
Place the cooled beef on top and wrap tightly into a log
Chill the wrapped beef in the refrigerator
Roll out puff pastry on a floured surface
Unwrap the beef and place it in the center of the pastry
Wrap the pastry around the beef and seal the edges
Brush the pastry with egg wash
Score the top lightly with a knife
Chill again briefly before baking
Bake in a preheated oven at 400°F until the pastry is golden and the beef reaches desired doneness
Rest the Wellington before slicing
Slice and serve immediately