Season tenderloin generously with salt and pepper.
Melt butter in a skillet over medium heat; add duxelles and cook until liquid has evaporated, ~25 minutes.
In a food processor, puree mushrooms, shallot, and thyme leaves. This mixture is referred to duxelles (duhk-uhlz)
Melt butter in a skillet over medium heat; add duxelles and cook until liquid has evaporated, ~25 minutes.
Place plastic wrap the length and width of the tenderloin on a work surface; overlap prosciutto on the plastic wrap, leaving no gaps, forming a rectangle big enough to cover the whole tenderloin.
Spread the duxelles evenly and thinly over the prosciutto; place tenderloin at one end of the prosciutto; roll all (not the plastic wrap!) to form a tight log, tucking the ends as you go. Now wrap this log in plastic wrap and twist ends tightly; refrigerate to chill.
Preheat oven to 425°F; on a lightly floured surface, roll puff pastry into a rectangle that will cover the tenderloin; brush with egg wash; remove tenderloin from plastic wrap and place at one end of puff pastry; tightly roll beef into pastry; press seam and ends to to
ensure a tight seal; trim off excess pastry.
ensure a tight seal; trim off excess pastry.
Transfer roll to a broiler pan or other pan that will allow the pastry bottom to breath; brush pastry with egg wash; cut several vents in the top of the pastry roll.
Bake until pastry is golden brown and the center registers 120°F for medium-rare, ~45 minutes; let rest 10 minutes before carving and serving.