Preheat oven to 400 degrees F.
Cut kielbasa into 6 (4-inch) pieces. Cut puff pastry sheets into thirds (6 strips). Roll each piece of kielbasa in puff pastry and place on a baking sheet.
Beat egg in a small dish and brush generously over pastry. Bake until pastry is golden brown and puffed, about 20 minutes. Serve with mustard, barbeque sauce, or jam, if desired.