1. For the sauce: Adjust oven rack to middle position and heat oven to 375 degrees. Process 1 can tomatoes with their juice in food processor until coarsely chopped with 1/4-inch pieces visible, 3 or 4 pulses. Transfer tomatoes to medium bowl. Repeat with remaining can tomatoes.
2. Heat oil, garlic, and pepper flakes (if using) in large saucepan over medium heat until fragrant but not brown, 1 to 2 minutes. Stir in tomatoes and salt and simmer until thickened slightly, about 15 minutes. Stir in basil; adjust seasoning with salt.
3. For the cheese filling: Combine ricotta, 1 cup Parmesan, mozzarella, eggs, salt, pepper, and herbs in medium bowl; set aside.
4. To assemble: Pour 1 inch boiling water in 13 by 9-inch broiler-safe baking dish, then add noodles 1 at a time. Let noodles soak until pliable, about 5 minutes, separating noodles with tip of sharp knife to prevent sticking. Remove noodles from water and place in single layer on clean kitchen towels; discard water in baking dish and dry baking dish.
5. Spread bottom of baking dish evenly with 1 1/2 cups sauce. Arrange 1 slice of prosciutto on each noodle. Using soupspoon, spread 1/4 cup cheese mixture evenly onto bottom 3/4 of each noodle on top of prosciutto (with short side facing you), leaving top 1/4 of noodle uncovered. Roll into tube shape and arrange in baking dish seam side down. Top evenly with remaining sauce, making certain that pasta is completely covered.
6. Cover manicotti with aluminum foil. Bake until bubbling, about 40 minutes, then remove foil. Remove manicotti and adjust oven rack to highest position (about 6 inches from heating element) and heat broiler. Sprinkle manicotti evenly with remaining 1 cup Parmesan. Broil until cheese is spotty brown, 4 to 6 minutes. Cool 15 minutes, then serve.
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