For the sauce: In a large bowl, use your hands to break up the tomatoes, squeezing them into 1/2-inch pieces. Set aside.
Place the pancetta in a large, heavy-bottomed saucepan or Dutch oven over medium-low heat. Cook gently until the pancetta releases its juices and browns, about 15 minutes. Remove with a slotted spoon and reserve.
To the rendered fat in the pan, add the olive oil and, when hot, the onions and 1/2 teaspoon salt. Cook until soft and golden, about 5 minutes. Add the garlic and cook just until it releases its fragrance, about 1 minute. Add the red pepper flakes and oregano, cook for a minute or two, and then add the red wine. Cook until the wine is almost evaporated, scraping up any browned bits from the bottom of the pan. Return the pancetta to the pan, along with the tomatoes and their juices, the carrots, and the basil. Bring to a boil, then reduce the heat to low and simmer gently, stirring frequently, until thickened and reduced by one-half to two-thirds, about 5 hours.
When the sauce has thickened and reduced, remove the carrots and basil, and puree to the desired smoothness using an immersion blender. Stir in the parsley.
For the meatballs: Preheat the oven to 450 degrees F. Spray a wire rack with nonstick cooking spray and place over a parchment-lined baking sheet.
Combine the panko and buttermilk in a large bowl and let sit, mashing occasionally with fork, until a smooth paste forms, about 10 minutes. Add the eggs, ground beef, ground pork, prosciutto, Parmesan, parsley, garlic, pepper and salt. Gently mix with your hands until thoroughly combined, then lightly form into golf ball-size meatballs (approximately 24).
Place the meatballs, evenly spaced, on the prepared rack and roast until browned, about 25 minutes, rotating the baking sheet halfway through.
When the sauce is ready, gently add the meatballs to the pot and simmer, covered, over low heat until the meatballs are fully cooked and firm, about 30 minutes.
Bring a large pot of well-salted water a boil--the water should taste salty like the ocean. Add the pasta and cook until just al dente. Drain and rinse under cold water, then return the pasta to the pot.
Ladle approximately half of the sauce into the pasta and simmer for 10 to 15 minutes, to let the pasta absorb some of the sauce.
Using tongs, portion the pasta into individual pasta bowls. Top with 3 to 4 meatballs per serving and finish with more sauce. Serve extra Parmesan separately at the table.