Preheat oven to 400 degrees and line a baking sheet with parchment paper.
Cut each hot dog into 6 pieces, about 1-inch long, for 36 pieces total.
Lightly flour your work surface. Roll out puff pastry to a rectangle about 12-inches by 10-inches.
With the longe edge towards you, cut the puff pastry vertically into 12 long strips. Then cut the strips horizontally into 3 sections, resulting in 36 strips.
Beat 1 egg with 1 tablespoon water.
Brush one end of a strip of puff pastry with the egg wash.
Starting at the end of the strip that does not have egg wash, roll up one hot dog piece in the puff pastry and place on the parchment-lined baking sheet seam side down.
Repeat with all strips of puff pastry and hot dog pieces.
Evenly brush all pigs in a blanket with egg wash and sprinkle with sesame seeds.
Bake until the puff pastry is golden brown, about 20 minutes.