Get the filling ready. In a small bowl, toss in the breadcrumbs, grated Parmesan cheese, chopped fresh parsley, minced garlic, and a pinch of salt and pepper. Stir to combine evenly.
Prepare the beef. If slices are not 1/4 inch thick, place between plastic wrap or in a zip-top bag and pound gently with a meat mallet or heavy pan until evenly thin.
Lay each beef slice flat. Divide the breadcrumb mixture among the four slices, spreading evenly and leaving a small border. If using, place a slice of provolone or mozzarella over the mixture on each piece.
Carefully roll up each beef slice tightly from a shorter end. Secure firmly with kitchen twine or toothpicks.
Heat the olive oil in a large, heavy skillet or Dutch oven over medium heat. Brown the beef rolls on all sides until they have a nice color.
Pour marinara or homemade tomato sauce over the browned beef rolls. Add red wine if using. Ensure braciole are mostly submerged.
Bring the sauce to a gentle simmer, then reduce heat to low, cover tightly, and cook for 1 1/2 to 2 hours, or longer, until beef is fork-tender.
Before serving, carefully remove the kitchen twine or toothpicks from each beef roll.
Serve hot, spooning sauce generously over the top. Garnish with a sprinkle of fresh basil or parsley.