Place beef between two pieces of plastic wrap. Gently pound to 1/4 to 1/8-inch thickness. Mince 4 cloves of garlic; slice the remaining 8 cloves. Combine minced garlic, parsley, cheese, breadcrumbs, salt and black pepper in a small bowl. Sprinkle filling evenly over all beef slices. Divide mushrooms evenly on the beef slices. Roll the beef into a cylinder, tucking in the sides to hold in the filling as you roll. Secure with toothpicks. Heat olive oil in a Dutch oven or large pot over medium-high heat. Place the beef rolls, seam side down in the pot and brown seam side first to seal it. Cook, turning the meat occasionally until each roll is nicely browned on all sides. Transfer to a plate. Combine the melted butter, Worcestershire sauce & Texas Pete together in a small bowl. Blend well. Brush butter mixture on the beef. Add the wine and the sliced garlic to the pot. Bring to a boil, scraping up any browned bits. Add beef broth, tomatoes and Italian seasoning. Place beef rolls back in the pot and bring back to a simmer. Cover and cook on low heat, turning occasionally until beef is tender and easily pierced with a fork, about 15 minutes. Remove beef from pot. Brush again with melted butter mixture. To thicken sauce, place pot back on the stove. Remove some of the hot cooking liquid to a bowl. Add the flour and stir until smooth to create a slurry. Slowly add it to the hot cooking liquid, bring to a slow simmer and cook until thickened. Serve thicken sauce over beef.