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In a heavy 6- to 8-quart saucepan, heat the olive oil over medium-high heat. Add the onion, celery, and fennel, stirring briefly. Let the vegetables sizzle for a moment in the oil, then lower the heat to medium-low. Cook the vegetables slowly, stirring occasionally, until softened and slightly browned, about 15 to 20 minutes.
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Raise the heat to medium and add the red pepper flakes and rosemary, stirring to incorporate. Stir in the lamb, then spread the mixture out in a single layer, letting the meat cook undisturbed for 5 minutes. Stir, lower the heat to medium-low, and cook for 15 minutes, stirring occasionally. The meat will slowly brown in some spots and a bit of a brown glaze will form at the bottom of the pan.
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Add the tomato paste, stir well, and cook for a few minutes. Deglaze the pan with the milk, scraping up any browned bits from the bottom of the pan with a wooden spoon. Simmer until the lamb has almost completely absorbed the milk.
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Add the wine, chicken stock, 2 cups of water, the rind of Parmigiano-Reggiano, and the bay leaf. Bring to a boil and then reduce to a low simmer, then cook, stirring occasionally, uncovered, for about 2 hours. If necessary, add 1⁄2 to 1 cup water toward the last half hour of cooking so that the lamb may simmer in enough liquid. The meat should be quite tender, with the finished ragu resembling a thick stew.
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Bring a large pot of salted water to a boil. Cook the rapini in the boiling water until just tender, about 3 minutes. Remove the greens using a slotted spoon to a rimmed baking sheet and set aside to cool; reserve the boiling water. When the greens are cool enough to handle, squeeze out the excess water and reserve the greens.
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Return the pot of water to a boil, add the rigatoni, and cook until almost al dente, about 3 minutes less than the package directs.
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While the pasta cooks, remove and discard the rind of Parmigiano-Reggiano and the bay leaf from the ragu. Remove half of the ragu from the saucepan and reserve for future use. Add the rapini and a small ladleful of the reserved hot water to the pot and keep the mixture warm over low heat.
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When the pasta is ready, drain it and reserve 1⁄2 cup of the cooking water. Add the rigatoni and 1⁄4 cup of the cooking water to the sauce, stirring to combine. Raise the heat to medium-high, and let the pasta finish cooking in the sauce at a quick simmer, stirring often. If necessary, adjust the thickness of the ragu with additional water. Stir in the butter. The ragu should be slightly wet, but viscous and shiny, just coating the pasta. Season to taste with salt and freshly ground pepper. Serve with grated Parmigiano-Reggiano.