Using kitchen twine, tie meat in 4 places. Season generously with salt and pepper.
Over high heat, coat bottom of a heavy pan with olive oil. Once pan is nearly smoking, sear meat until well-browned on all sides, including the ends, about 2 minutes per side (12 minutes total).
Transfer to a plate. When cool enough to handle, snip off twine and coat all sides with mustard. Let cool in fridge.
Place plastic wrap down on a work surface, overlapping so that it’s twice the length and width of the tenderloin. Place the prosciutto on the plastic wrap into a rectangle that’s big enough to cover the meat. Spread the duxelles evenly and thinly over the prosciutto.
Season meat again, then place it at the bottom of the prosciutto. Roll meat into prosciutto-mushroom mixture, using plastic wrap to roll tightly. Tuck ends of prosciutto as you roll, then twist ends of plastic wrap tightly into a log and transfer to fridge to chill (this helps it maintain its shape).
Heat oven to high. Lightly flour your work surface, then spread out puff pastry and roll it into a rectangle that will cover the meat log.
Remove meat roll from plastic wrap and place on a sheet of puff pastry. Brush the edges of the pastry with egg wash, then tightly roll beef into pastry.
Once the log is fully covered in puff pastry, trim any extra pastry, then crimp edges with a fork to seal well. Wrap roll in plastic wrap to get a really tight cylinder, then chill for 20 minutes.
Remove plastic wrap, then transfer roll to a foil-lined baking sheet. Brush with egg wash and sprinkle with flaky salt.
.Bake until pastry is golden - about 40 to 45 minutes for medium. Let rest 10 minutes before carving and serving.