Preheat the oven to 400°F/204°C and line a Sheet Pan with parchment paper.Check the salmon for pin bones, removing any that you find with tweezers, then cut in half lengthwise, so you have 2 sides that you can sandwich back together. Mix the softened butter with the parsley, basil, dill, lemon zest, Kosher sea salt, and freshly cracked black pepper.
Pat the salmon fillets dry with a paper towel, then season lightly with salt and pepper. Spread the herb butter over one fillet, and the mustard evenly on the other fillet. Sandwich the two salmon fillets together, in opposite directions so both ends are of an even thickness.
Roll out the pastry thinly on a lightly floured surface to a rectangle, the thickness of a nickel coin and large enough to enclose the salmon. Put the salmon parcel in the center of the pastry and brush the surrounding pastry with egg. Bring up the edges, trimming off any excess, and tuck them in before folding the rest of the pastry over to form a neat parcel. Carefully turn the whole thing over so that the seam is underneath and place on the parchment-lined sheet pan. Lightly score a cross-hatch pattern using the back of a knife. Cover loosely and chill for 15 minutes. Brush the pastry with beaten egg.
Bake the salmon for 20-25 minutes, until the pastry is golden and crisp. To test for doneness, insert a skewer into the middle. It should feel warm for medium cooked salmon. A piping hot skewer indicates that the fish is well done. We shoot for medium doneness with this dish every time.
Allow the salmon to rest for 5 minutes, then cut into portions using a straight-edged knife. Wiped clean between slicing.