Combine the bread and milk in a large bowl and let soak, 15 minutes.
Meanwhile, make the sauce: Cook the olive oil, smashed garlic and red pepper flakes in a large pot over medium-high heat, stirring, until the garlic softens, about 2 minutes. Stir in the tomato paste and cook until it begins to sizzle, about 2 minutes. Add the strained tomatoes, bay leaves and 5 cups water; bring to a boil and cook 20 minutes. Place the beef slices between 2 pieces of plastic wrap and pound with a heavy skillet until 1/16 inch thick. Position the slices with the short sides facing you and lay a slice of prosciutto on top of each. Add 1/2 cup parsley, the pecorino and minced garlic to the soaked bread and mix with your hands, breaking up the bread; spread on top of the prosciutto. Cut the provolone into twelve 2-to-3-inch-long sticks, about 1/2 inch thick. Put a piece of cheese horizontally across the middle of each slice of beef and trim any overhanging cheese. Starting with a short end, tightly roll up the beef and secure with a toothpick. Transfer the braciole to the sauce. Reduce the heat to medium low, cover and simmer 1 hour. Uncover, stir and reduce the heat to low; continue simmering, uncovered, until the beef is tender and the sauce thickens, 1 more hour. (Add up to 1 cup water if the sauce gets too thick.) Discard the bay leaves. Stir in the remaining 1/4 cup parsley and season with salt. About 20 minutes before serving, bring a large pot of salted water to a boil. Add the pasta and cook as the label directs. Remove the braciole from the sauce and transfer to a platter; remove the toothpicks. Pour half of the sauce on top. Drain the pasta and toss with the remaining sauce. Serve the braciole with the pasta; top with pecorino. Photograph by Anna Williams