Season the beef tenderloin with salt and pepper, then sear in a hot pan with olive oil until browned on all sides; remove and immediately brush with Dijon mustard.
Finely mince the mushrooms, shallot, and garlic, then sauté in the same pan with thyme until all moisture has evaporated and the mixture is dry.
Lay a sheet of plastic wrap on a clean surface and arrange the prosciutto slices in an overlapping rectangle.
Spread the mushroom duxelles evenly over the prosciutto, place the beef at the edge, and roll it tightly into a log using the plastic wrap to assist.
Chill the beef log in the refrigerator for 20 minutes to firm up.
Roll out the puff pastry on a 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 little beaten egg, and place seam-side down on a baking sheet.
Brush the entire pastry with the remaining egg wash, score the top lightly with a knife, and bake at 425°F for 20-25 minutes until the crust is golden brown.