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Preheat the broiler. Meanwhile, using the tip of a knife, score the eggplant deeply and sprinkle with salt. Place the eggplant cut-side up and cook under the broiler until lightly browned, about 4 minutes. Remove the eggplant from the broiler and place on a plate and microwave on high until tender, about 2 minutes. Let cool.
In a large bowl, add the meats and mix gently to incorporate. Place the egg white, remaining chicken stock, onion, garlic and parsley in the beaker of a blender and blend until smooth, about 30 seconds. Add the mixture to the bowl with the meats, add the cheese and crumble the kamut in with your fingers. Sprinkle with salt and chili flakes.
Scoop the eggplant pulp out of its skin and let any excess water drip off. Measure out 1/2 cup of the pulp, and then lightly chop and add to the meat mixture, folding in to incorporate. With the use of a tablespoon, measure out 16 even heaping mounds on to a clean work surface and then form into balls with your hands.
Spray a large nonstick saute pan with 4 sprays of olive oil spray and heat over medium-high heat. Once the pan is hot, add half of the meatballs and cook until lightly browned on one side, about 1 minute. Roll the meatballs on the other side and brown evenly, about 2 minutes. Remove the browned meatballs from the pan and then spray the pan with 4 more sprays and repeat the browning with the rest of the meatballs. Add the meatballs to the sauce and simmer very slowly for an hour.
Meanwhile, bring 4 quarts of water to a simmer and then add 1 tablespoon of salt. Drop the pasta in the water and cook per manufacturer's instructions. Place 4 meatballs each on 4 plates, and then add the spaghetti to the remaining sauce in the pan with 1/2 cup of the pasta water and cook until the sauce holds well on the pasta. Evenly distribute the pasta to each of the 4 plates.