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Step 1
Whisk together the breadcrumbs, Parmesan, parsley, chopped basil and 1/2 teaspoon of pepper in a medium bowl. Add 4 tablespoons of the olive oil to a small bowl. Grate 3 cloves of garlic into the olive oil and whisk to combine. Pour the olive oil mixture into the breadcrumb mixture and fluff with a fork until the mixture is evenly combined and resembles wet sand.
Step 2
Arrange one slice of beef on a clean work surface. Top with 1 slice of prosciutto, folding if necessary to fit the slice of meat. Top the prosciutto with 2 tablespoons of the breadcrumb mixture and press slightly to compact it. Fold in the side edges of the beef about a 1/4 inch. Starting from the bottom, roll up the beef like a jelly roll, creating a cylinder. Secure the opening with 2 toothpicks. Place the finished roll on a rimmed baking sheet and continue the process with the remaining meat, prosciutto and breadcrumb mixture. Once all the meat is rolled, season with 1/2 teaspoon salt and 1/2 teaspoon pepper.
Step 3
Add the remaining 3 tablespoons of olive oil to a large high-sided pan and heat over medium. Once the oil is shimmering add the beef rolls, in batches, being sure not to overcrowd the pan. Brown on both sides, about 2 minutes. Remove to the rimmed baking sheet and brown the remaining rolls.
Step 4
Once all the rolls have been browned and removed from the pan, add the red wine. Cook, scraping up any brown bits from the bottom of the pan, until the harsh alcohol smell burns off and the wine slightly reduces, about 2 minutes. Next, add the tomatoes, basil sprigs, red pepper flakes, 1/4 teaspoon salt and the remaining 2 cloves of garlic. Stir to combine. Add 1/2 cup water to the can of tomatoes and swirl it around to clean any residual tomato from the sides of the can. Add the tomato water to the pan. Bring the mixture to a simmer, then add the rolls back to the pan and turn the heat down to low. Baste the meat in the tomato sauce, cover the pan and cook on low, basting the meat 2 to 3 times during the cooking process, until the meat is very tender, 1 hour 45 minutes to 2 hours.
Step 5
To serve, remove the toothpicks from the rolls and serve topped with red sauce and freshly grated Parmesan.