In a small saute pan, add 1 tablespoon olive oil, onions, and garlic and cook until translucent. Remove and let cool.
Tenderize flank steak with a meat mallet and cut into 1/4-inch pieces, approximately 5 by 8 inches long. Lightly season with salt and freshly ground black pepper.
Place carrots, red bell peppers, sun-dried tomato, and green onions in separate layers over the first 5 inches of the steak lengthwise. Top with garlic and onion mixture, then evenly coat with shredded mozzarella cheese and parsley.
Roll flank steak, starting with end that has vegetables, firmly without pushing out vegetables. Secure rolled steak with skewers.
To a rimmed plate stir the flour and Italian seasoning together and dredge the rolled flank steak, coating evenly.
Preheat oven to 300 degrees F.
In a medium saute pan heat 2 tablespoons olive oil and when hot add the rolled flank steak, searing on all sides for about 4 to 5 minutes until golden brown. Remove the flank steak from the pan and place on a baking sheet. Place in preheated oven for 15 minutes or until internal temperature reaches 135 degrees F. on an instant-read thermometer.
Place the saute pan back on burner and deglaze with the white wine. Stir, and reduce for 2 minutes, then add tomato sauce and chicken stock. Let mixture continue to reduce for 2 more minutes. Remove the steak from the oven and let rest. Slice on the bias 1/2-inch, shingle out, and top with sauce.