Preheat oven to 400 degrees and line a baking sheet with parchment paper.
Thoroughly combine shredded cheese, cream cheese, green onions, dijon and garlic in a medium bowl.
Cut each hot dog into 5 pieces, about 1-inch long, for 30 pieces total.
Lightly flour your work surface. Roll out the puff pastry to a rectangle about 12-inches by 10-inches.
With the long edge towards you, cut the puff pastry vertically into 6 long strips. Then cut the strips horizontally into 5 sections, resulting in 30 squares.
Evenly spoon the cheese mixture into the center of each square, about ½ teaspoon per square.
Beat egg with 1 tablespoon water.
Brush the top right corner of the square with egg wash.
Pace a hot dog piece horizontally ontop of the cheese mixture.
Wrap two corners around the hot dog with the egg wash corner on top to seal the puff pastry and place on the parchment-lined baking sheet.
Repeat with remaining ingredients.
Evenly brush all pigs in a blanket with egg wash.
Bake until the puff pastry is golden brown, about 25 minutes.
Serve immediately!