Heat a large skillet over medium-high heat. Cook and stir sausage in the hot skillet until browned and crumbly, 5 to 7 minutes. Drain and discard grease.
Preheat oven to 375 degrees F (190 degrees C).
Combine cooked sausage, Jack cheese, carrots, eggs, green onions, Parmesan cheese, mustard, pepper, and Italian seasoning in a large bowl.
Roll out dough onto a 9x13-inch baking pan. Separate into 8 rectangles; press perforations together to seal. Spoon 1/3 cup sausage mixture onto each rectangle; fold dough over the mixture and press edges to seal.
Bake in the preheated oven until golden brown, 18 to 20 minutes.