Pound the beef cutlets 1/4-inch thin. Add the cheese, parsley and garlic to a small bowl and toss. Divide evenly over each cutlet. Roll up each cutlet and tie with butcher's twine to secure and to make a roll. Sprinkle each roll with salt and pepper.
Heat 2 tablespoons olive oil in a large, heavy-bottomed Dutch oven over medium-high heat. Add the beef rolls and the cubed beef and brown on all sides. Remove to a plate once browned. Add a touch more olive oil to the pan and add the carrots and onions and saute until tender. Add the wine and simmer for a minute or so, and then scrape up the browned bits on the bottom of the pan. Stir in the passata and bay leaves. Bring to a simmer, add the beef back into the pot and cover with a lid. Cook on low until thick and the meat begins to fall apart, flipping the rolls occasionally, 2 1/2 to 3 hours. (If too dry, add a half cup of water; if too loose, remove the lid to finish thickening).
Bring a large pot of salted water to a boil. Add the orecchiette, cook until al dente and drain.
Remove the bay leaves and discard from the sauce. Carefully remove the braciole to a cutting board and cut off the butcher's twine. Slice the beef rolls into rounds. Add the pasta to the sauce and toss all together. Serve on a large platter and top with the braciole rounds and sprinkle with lots of pecorino cheese.
Use canned crushed tomatoes if you cannot find passata di pomodoro.
Recipe courtesy of Gabriele Corcos and Debi Mazar, Extra Virgin, 2011