Heat oven to 375°F. Spray cookie sheet with cooking spray.
If using crescent rolls: Unroll dough; separate into 4 rectangles. Place on cookie sheet. Press each into 6x4-inch rectangle, firmly pressing perforations to seal. If using dough sheet: Unroll dough; cut into 4 rectangles; place on cookie sheet. Press each into 6x4-inch rectangle.
Spread 1 teaspoon mustard over each rectangle to within 1/2 inch of edges. Place 1/4 cup sauerkraut and 1 bratwurst lengthwise down center of each rectangle.
On long sides of each rectangle, make 5 cuts at an angle and 1 inch apart almost to edge of sauerkraut. For braided appearance, fold strips of dough at an angle across bratwurst with ends of strips slightly overlapping, alternating from side to side; press ends to seal. Brush tops with egg; sprinkle with caraway seed.
Bake 15 to 20 minutes or until deep golden brown. Immediately remove from cookie sheet. Serve warm with additional mustard, if desired.