Adjust oven rack to lower-middle position and heat oven to 325 degrees. Stir 3 tablespoons oil, half of garlic, lemon zest, and anchovies together in medium bowl. Add ⅓ cup basil, parsley, Pecorino, and bread crumbs and stir to incorporate. Stir in fontina until evenly distributed and set aside filling.
Halve steak against grain to create 2 smaller steaks. Lay 1 steak on cutting board with grain running parallel to counter edge. Holding blade of chef's knife parallel to counter, halve steak horizontally to create 2 thin pieces. Repeat with remaining steak. Cover 1 piece with plastic wrap and, using meat pounder, flatten into rough rectangle measuring no more than ¼ inch thick. Repeat pounding with remaining 3 pieces. Cut each piece in half, with grain, to create total of 8 pieces.
Lay 4 pieces on cutting board with grain running parallel to counter edge (if 1 side is shorter than the other, place shorter side closer to you). Distribute half of filling evenly over pieces. Top filling on each piece with 1 slice of prosciutto, folding to fit, and press firmly. Keeping filling in place, roll each piece away from you to form tight log. Tie each roll with 2 pieces kitchen twine to secure. Repeat process with remaining steak pieces, filling, and prosciutto. Sprinkle rolls on both sides with salt and pepper.
Heat remaining ¼ cup oil in large Dutch oven over medium-high heat until shimmering. Brown rolls on 2 sides, 8 to 10 minutes. Using tongs, transfer rolls to plate. Add onion to pot and cook, stirring occasionally, until softened and lightly browned, 5 to 7 minutes. Stir in pepper flakes and remaining garlic; cook until fragrant, about 30 seconds. Stir in tomato paste and cook until slightly darkened, 3 to 4 minutes. Add wine and cook, scraping up any browned bits. Stir in tomatoes and broth. Return rolls to pot; bring to simmer. Cover and transfer to oven. Braise until meat is fork-tender, 2½ to 3 hours, using tongs to flip rolls halfway through braising.
Transfer braciole to serving dish and discard twine. Stir remaining 2 tablespoons basil into tomato sauce and season with salt and pepper to taste. Pour sauce over braciole and serve, passing extra Pecorino separately.
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