Preheat the oven to 400 degrees F.
Bake the sausage on a baking sheet for 20 minutes. Turn the sausage and bake for 5 to 10 minutes more, until it's fully cooked. Cool to room temperature.
Unfold the puff pastry on a lightly floured board. Cut each piece in 1/2 lengthwise and brush the top sides with mustard. Divide the sausage into 4 equal pieces. Starting at the long end of the pastry, place 1 piece of the sausage on top of the mustard and roll it up tightly, overlapping the end by 1/2-inch and sealing the pastry by brushing the edge with water. Cut off the excess pastry. Roll the other 3 pieces of sausage in puff pastry. Place the 4 rolls, seam side down, on a baking sheet lined with parchment paper. Brush with the egg wash. Lightly score each roll diagonally to make 7 equal pieces. Bake for 20 to 25 minutes, until browned. Slice and serve hot with mustard.
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