Preheat the oven to 375 degrees.
Lay the cold puff pastry on a board and cut a 5½-inch wide strip to match the length of the hot dogs. Brush a 3-inch-wide strip of the cut pastry generously with Dijon mustard. Place a hot dog at the end of the pastry where you brushed the mustard and roll it up and away from you one turn, until the hot dog is just encased in one layer of pastry and mustard. Brush the next 1-inch strip of pastry with the egg wash and continue to roll the hot dog, so the pastry is completely sealed. Cut any remaining pastry across and place the hot dog, seam side down, on a sheet pan lined with parchment paper. Prepare the remaining 3 hot dogs the same way.
Brush the pastry with egg wash and sprinkle generously with sea salt and pepper. Bake for 15 to 20 minutes, until the pastry is nicely browned. Serve hot with extra mustard on the side.
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