Arrange an oven rack in the center of the oven and preheat to 450 degrees F.
Warm the marinara and meatballs in a medium saucepan over medium-low heat, about 10 minutes. Remove 1 cup of the sauce and reserve.
Meanwhile, bring a large pot of salted water to a boil and cook the udon noodles according to package instructions; drain.
Roll a 24-inch piece of foil into a prism shape. Crumble and flatten 2 more 24-inch pieces of foil into an 8-by-4-inch oval shape. Place the prism in the center of a 10-cup heatproof bowl and bend the ends so that the foil is pressed against the bowl and divides the bowl in half (this will make the 2 hemispheres of a brain). Place the 2 foil ovals on either side of the prism. Cover all 3 with an 18-inch piece of foil, pressing it into the foil barrier shapes. This is the brain mold. Generously spray the mold with nonstick spray.
Whisk the mozzarella, eggs, reserved sauce and 1/4 cup of the Parmesan in a large bowl until combined. Add the noodles to the egg mixture and toss until evenly coated. Transfer half of the noodles to the mold, pressing gently to create a well in the center of the noodles. Cover the well with half of the prosciutto (do to not let it touch the foil or it will stick). Fill the well with the meatballs (leaving remaining sauce behind) and then top with the remaining prosciutto, forming gently to create a pocket of meatballs in the center of the brain. Top with the remaining noodles and arrange so that they fill in all the gaps, surround the meat and are pressed firmly against the walls of the mold. Toss the breadcrumbs with the oil and remaining 1/4 cup Parmesan in a small bowl, then evenly sprinkle over the noodles, pressing them down into the noodles to adhere.
Bake until the breadcrumbs are a deep golden brown and the noodles have completely set, 30 to 40 minutes. Let sit in the mold for 30 minutes before removing. Invert onto a cutting board and pour the remaining sauce down the center channel of the brain.
Pre-cooked udon noodles are generally plumper than the kind you can cook up from dried. You can find them in the frozen section of many Asian grocery stores.
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