Tomato Sauce

• 10 medium garlic cloves, peeled
• 3/4 cup loosely packed fresh basil leaves, plus small basil leaves for garnish
• 1/2 cup extra-virgin olive oil
• 1/4 teaspoon crushed red pepper
• 1/2 cup (4 ounces) unsalted butter
• 1 medium (10 ounces) yellow onion, peeled and halved lengthwise with root end intact
• 2 (28-ounce) cans crushed San Marzano tomatoes or whole peeled tomatoes, hand-crushed
• 1 cup water
• 1 (3-inch) Parmigiano-Reggiano cheese rind
• 1 1/2 teaspoons kosher salt

Braciole

• 2 tablespoons unsalted butter
• 1 cup panko (Japanese-style breadcrumbs)
• 2 teaspoons fresh thyme leaves
• 1 tablespoon plus 1/4 teaspoon kosher salt, divided
• 2 (1 1/2 pound each) flank steaks, butterflied and pounded 1/4-inch thick
• 2 teaspoons freshly ground black pepper, divided
• 4 ounces thinly sliced prosciutto  (about 8 slices)
• 1/4 cup toasted pine nuts
• 1/4 cup fresh flat-leaf parsley, finely chopped, plus more for garnish
• 3 tablespoons garlic, finely chopped
• 2 1/4 ounces Parmigiano-Reggiano cheese, grated (about 1/2 cup plus 1 tablespoon)
• 2 1/4 ounces Pecorino Romano cheese, finely shredded (about 1/2 cup plus 1 tablespoon)
• 3 tablespoons olive oil