Preheat oven 400 degrees. Line a baking sheet with parchment paper. In a small bowl mix the egg with 1 tbsp water.
Roll out each piece of puff pastry and cut each one in half so you have 4 pieces. Make sure each piece can completely go around the brats.
Spread each piece of puff pastry with mustard. Top with sauerkraut then cheese. Lay the brat on top. Brush the sides with egg wash and fold the pastry around the brat sealing the ends. Lay seam side down on baking tray. Completely brush the whole dog with egg wash and sprinkle the caraway seeds on top. Repeat with the remaining brats. Bake about 20 minutes until browned