Bring garlic, basil, oil, and crushed red pepper to a simmer in a small saucepan over medium-low; cook until basil wilts but remains green, 2 to 3 minutes. Remove from heat; set aside, and let cool slightly, about 15 minutes.
Transfer garlic mixture to a blender, food processor, or use an immersion blender; process until smooth, about 30 seconds. Set aside.
Melt butter in a large saucepan over medium. Add onion, cut side down; cook, undisturbed, until onion starts to brown, 4 to 5 minutes. Add tomatoes and water (add about 1/2 cup water to each crushed tomato can, swishing to loosen any remaining sauce); bring to a simmer over medium-high. Add cheese rind, and reduce heat to medium-low. Cook, uncovered, stirring occasionally, until sauce is thickened and slightly reduced, about 40 minutes. Remove and discard cheese rind and onion. Add reserved garlic mixture and salt to tomato sauce, stirring to combine. (If making in advance, let cool completely, and transfer to an airtight container. Store in refrigerator for up to 1 week.)
Melt butter in a medium skillet over medium. Add panko, and cook, stirring often, until golden brown and toasted, about 3 minutes. Transfer to a heatproof bowl, and stir in thyme and 1/4 teaspoon of the salt; set aside.
Preheat oven to 325°F. Lay steaks flat on a clean work surface or parchment paper. Sprinkle top of each steak with 3/4 teaspoon of the salt and 1/2 teaspoon of the pepper. Divide prosciutto evenly between steaks, overlapping in a single layer across steaks. Sprinkle reserved panko mixture evenly over steaks; sprinkle evenly with pine nuts, parsley, garlic, and 1/2 cup each of the Parmigiano-Reggiano and Pecorino Romano. Roll up each steak over filling, rolling against the grain of steak; cut in half crosswise. Using skewers or kitchen twine, secure rolled steaks. Sprinkle each steak with remaining 3/4 teaspoon salt and 1/2 teaspoon pepper.
Heat oil in a large high-sided, heatproof skillet or Dutch oven over medium-high. Add steaks, and cook, turning occasionally, until browned on all sides, about 2 minutes per side. Transfer steaks from skillet to a large plate. Wipe skillet clean. Add reserved tomato sauce to skillet, and nestle steaks into sauce, spooning some of sauce over steaks.
Cover and bake in preheated oven until steak is very tender, 1 hour, 30 minutes to 2 hours, turning steaks halfway through baking time. Transfer steaks to a large cutting board, and let cool for 10 minutes. Spoon some of sauce in skillet onto a platter. Cut steaks evenly into medallions, and arrange over sauce. Spoon additional sauce over steaks, and garnish with basil, parsley, and remaining 1 tablespoon each Parmigiano-reggiano and Pecorino Romano. Serve immediately with any remaining sauce on the side.
