Season tenderloin generously with salt and pepper, then wrap tightly in plastic wrap and let rest in refridgeratorfor at least 20 minutes, but preferably about 2 hours.
Heat olive oil in a heavy skillet over high heat. Once pan isnearly smoking, sear tenderloin until well-browned on all sides, including the ends - about 2 minutes per side (less if you like it more rare). Transfer to a cutting boar or plate to cool. When cool enough to handle, coat all sides with mustard. Wrap tightly in plastic wrap again and return to fridge to rest.
In a food processor, finely chop shallots. Add shallots to skillet over medium heat with butter and saute until translucent.
Chop mushrooms and thyme in the food processor until finely chopped. Add to skillet with shallots and cook until liquid has evaporated, stirring occasionally, about 25 minutes. Season with salt and pepper, spread out flat on a cooking tray, then let cool in the fridge.
Place plastic wrap down on a work surface, overlapping so that it’s twice the length and width of the tenderloin. Arrange the prosciutto on the plastic wrap into a rectangle that’s big enough to cover the whole tenderloin. Spread the duxelles evenly and thinly over the prosciutto.
Place tenderloin at the bottom of the prosciutto. Roll meatinto 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 the fridge to chill for 10-20 minutes.
Heat oven to 425°. Lightly flour your work surface, then spread out puff pastry and roll it into a rectangle that will cover the tenderloin (just a little bigger than the prosciutto rectangle you just made!). Remove tenderloin from plastic wrap and place on bottom of puff pastry. Brush the other three 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 crimpedges 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 and the center registers 120°F for medium-rare - about 40 to 45 minutes. Let rest 10 minutes before carving and serving.
