Preheat the oven to 450 degrees. Place a piece of parchment paper on a sheet pan.
Lay one sheet of puff pastry on a floured board and lightly roll into a 10-inch square. Place it on the sheet pan and brush the pastry with all the mustard, leaving a 1-inch border. Arrange the soppressata in overlapping layers on the mustard and sprinkle the grated cheese evenly on the soppressata, also avoiding the border. Brush the border with the egg wash.
Lightly roll the second piece of puff pastry into a 10-inch square. Lay the pastry directly on top of the first square, lining up the edges. Brush the top with the egg wash, cut three large slits for steam to escape, and chill for 15 minutes.
When the pastry is cold, trim the edges with a very sharp knife to make a clean edge. Bake the pastry in the center of the oven for 20 to 25 minutes, turning once while baking, until puffed and brown. Allow to cool for a few minutes, cut in squares, and serve hot or warm.
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