Place the beef slices between two pieces of plastic wrap and pound gently with a meat mallet to flatten and even out the slices. Season each steak with salt, ground black pepper, and red pepper flakes, about ¼ teaspoon of each to each slice.

Sprinkle each slice of meat with minced garlic, grated parmesan cheese, and parsley. Top each slice of meat with a slice of prosciutto and provolone cheese if using. Starting at 1 short end, roll up the steak as for a jelly roll to enclose the filling completely. Using butcher's twine, tie the steak roll to secure or fasten rolled meat with plain toothpicks. Repeat this process with the remaining beef and filling.

Coat a large, wide nonstick pot with olive oil and put over medium-high heat. Season each beef braciole generously with salt and pepper and place in the pot; it should sizzle when it touches the oil. Turn heat down to medium-low and add the 4 smashed garlic cloves to the pot to infuse the oil (you can leave the skins on) on either side of the beef braciole.

Brown meat on all sides, 2 to 3 minutes per side. Remove them from the pan and reserve. Discard the smashed garlic.

In the same pan, heat 2 tablespoons of extra virgin olive oil over medium heat. Add the onions and season with 1 teaspoon of kosher salt, and ½ teaspoon red pepper flakes (adjust to taste). Cook the onions until they are translucent and very aromatic, about 8 to 10 minutes.

Add the garlic and saute for another 2 minutes. Add the tomato paste and cook for 3 more minutes. Then deglaze the pan with the wine, scraping all the fond from the bottom, and cook for 6 to 8 minutes.

Add the tomatoes and 2 cups of water and bring to a simmer, and then add the meat back to the pan. Simmer, occasionally stirring over low heat until the meat is tender, about 1-½ hours.

Uncover, add the mushrooms and stir in the remaining ¼ cup parsley and basil. Reduce the heat to low; continue simmering, uncovered, and occasionally stirring until the beef is tender and the sauce thickens, ½ hour to 1 more hour. Taste and adjust season if needed.

About 20 minutes before serving, bring a large pot of salted water to a boil. Add the pasta and cook as the label directs. (Here's How to Make Buttered Pasta).

Remove the Beef Braciole from the sauce and transfer to a platter; remove the toothpicks or butcher's twine. Spoon on some of the sauce and garnish with chopped parsley. Serve the Beef Braciole with a side of Buttered Pasta; top with grated Parmigiano-Reggiano cheese.