Grill brats according to package directions. Let cool.
Preheat oven to 400 degrees and line a baking sheet with parchment paper.
Place puff pastry on a lightly floured surface and roll out slightly. When cut in quarters, each piece should be about as long as a bratwurst.
Cut puff pastry into 4 equal quarters. Place on prepared baking sheet.
Place 1 1/2 slices Swiss cheese to cover each piece of puff pastry.
Spread 1 teaspoon of Dijon mustard on top of cheese for each piece of puff pastry.
Arrange 1/4 cup sauerkraut down the center of each piece and place the bratwursts on top.
Roll puff pastry around bratwurst and place seam side down.
Whisk egg with 1 tablespoon water and brush egg mixture across the top of the puff pastry.
Sprinkle with caraway seeds.
Place in oven and bake for 20 to 24 minutes, or until golden brown.
Serve with mustard.