Prepare the Filling: In a small bowl, mix breadcrumbs, Parmesan cheese, parsley, minced garlic, salt, and pepper. Set aside.
Assemble the Braciole: Lay out the beef slices on a flat surface. Spread a thin layer of the breadcrumb mixture over each slice. Roll the beef tightly and secure with kitchen twine or toothpicks.
Sear the Rolls: Heat olive oil in a large skillet over medium-high heat. Brown the beef rolls on all sides, then transfer them to a plate.
Make the Sauce: In the same skillet, sauté onion and garlic until fragrant. Deglaze the pan with red wine if using. Add crushed tomatoes, oregano, sugar, salt, and pepper. Stir to combine.
Simmer the Braciole: Return the beef rolls to the skillet, ensuring they’re submerged in the sauce. Cover and simmer on low heat for 2 hours, occasionally stirring.
Serve: Remove twine or toothpicks before serving. Garnish with fresh basil and additional Parmesan cheese.