On a large piece of plastic wrap (you may want to double layer the plastic wrap), lay out the prosciutto in slightly overlapping layers to form a square that will be large enough to wrap the tenderloin in. Spread the duxelles mixture evenly over the prosciutto, then place the tenderloin on one end.
Use the plastic wrap to help you roll up the tenderloin in the prosciutto and mushrooms, wrapping it tightly to form a log. Tuck in the ends of the prosciutto as you roll it up. Twist the ends of the plastic wrap closed, then place the tenderloin in the fridge for 30 minutes to help make sure it will all hold together.
Preheat oven to 425°F (218°C).
Lightly dust a clean surface with flour then roll out the thawed puff pastry, pressing the edges together to seal if working with two sheets. It should create a rectangle large enough to wrap the prosciutto-wrapped tenderloin roast.
Remove the tenderloin from the plastic wrap, then place on the puff pastry. Roll it up, tucking the ends under and brushing the beaten egg over the long edge to seal the seam. If you find that you have significant excess pastry along the edges, you may want to trim some of that away.
Transfer the wrapped beef wellington to a large baking sheet lined with parchment paper. Brush the top with the remaining egg wash, then cut diagonal slashes every inch or so down the length of the pastry to allow steam to vent while the wellington is baking. Sprinkle with flaky salt or coarse sea salt.
Bake until golden brown on the outside and the tenderloin reaches 120-125°F (49-51°C) on a digital meat thermometer for medium-rare doneness. This is typically around 40 to 45 minutes, depending on the size of your tenderloin roast. Remove from the oven and rest for 10 minutes before slicing into thick slices.
Serve slices garnished with the fresh minced chives and an additional sprinkling of flaky or coarse salt.