Using kitchen twine, tie tenderloin in 4 places. Season generously with salt and pepper. Over high heat, coat bottom of a heavy skillet with olive oil. Once pan is nearly smoking, sear tenderloin 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.

Meanwhile, make duxelles: In a food processor, pulse mushrooms, shallots, and thyme until finely chopped. To skillet, add butter and melt over medium heat. Add mushroom mixture and cook until liquid has evaporated, about 25 minutes. Season with salt and pepper, then 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. Spread the duxelles evenly and thinly. Season tenderloin, then place it at the bottom of the mushroom mixture. Roll meat into mushroom mixture, using plastic wrap to roll tightly. Tuck ends of 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 425°. Lightly flour your work surface, then spread out puff pastry and roll it into a rectangle that will cover the tenderloin. 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 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 and the center registers 120°F for medium-rare, about 25-35 minutes. Let rest 10 minutes before carving and serving.