For the lamb:
Generously season the lamb all over with salt and pepper; set aside.
In a Dutch oven or a heavy-bottomed 6-quart pot with a tightfitting lid, heat the oil over medium-high heat until shimmering. Cook the lamb in three batches (so as not to crowd the pot) until browned on all sides, about 5 minutes per batch. Transfer to a large bowl; set aside.
Reduce the heat to medium, add the onion, garlic, oregano, cinnamon, and measured salt to the pot, and sauté, stirring occasionally, until the onion is softened and fragrant, about 5 minutes. Add the tomato paste, stir to coat the onion, and cook until the tomato paste is no longer raw-tasting, about 2 minutes. Stir in the wine and cook until reduced by half, about 4 minutes. Stir in the tomato sauce, 2 cups of the water, and the bay leaves. Return the lamb pieces to the pot along with any accumulated juices. Bring to a simmer over high heat, lower the heat, cover, and simmer for 1 hour. Using tongs, rotate the lamb pieces from the bottom of the pot to the top, cover, and simmer until the meat is falling off the bone, about 1 hour more.
Transfer the lamb to a serving dish and cover with foil. Keep warm at room temperature or in a 200°F oven.
Strain the braising liquid through a fine-mesh strainer into a medium bowl or large measuring cup. Skim the fat from the surface (alternatively, you can use a fat separator) and discard; you should have about 4 cups of liquid remaining. Place the liquid back in the pot and bring to a simmer over medium heat. In a small bowl, stir together the remaining 6 tablespoons water and the cornstarch and add it to the braising liquid. Simmer until the sauce has thickened, about 1 minute. Pour over the lamb or serve on the side with the pasta.
For the pasta:
Bring a large pot of salted water to a boil over high heat. Add the pasta, stir, and cook until al dente, about 5 minutes; drain and set aside. Using a paper towel, dry the inside of the pot.
Return the pot to high heat, add the oil, and heat until shimmering, about 2 minutes.
Remove the pot from heat, add the cooked pasta, and sprinkle with half of the cheese. Toss the pasta with tongs. Sprinkle the remaining cheese on the pasta, toss to coat, and serve with the lamb and sauce.
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