How to Make It
Microwave the duck legs at high power for 1 minute, until warm. Remove the skin from the legs and reserve it for another use. Remove the meat from the bones and cut it into bite-sized pieces; discard the bones.
In a large, deep skillet, heat the oil. Add the onion, carrot and celery and season lightly with salt and pepper. Cook over moderately high heat, stirring, until slightly softened, 1 minute. Reduce the heat to moderate and cook, stirring, until browned, about 8 minutes. Add the olives, rosemary and garlic and cook over high heat, stirring, until fragrant, about 1 minute. Add the duck and stir gently to coat with the vegetables. Add the wine and simmer for 1 minute. Add the stock and simmer until the liquid is reduced to 3/4 cup, about 10 minutes. Remove from the heat and stir in half of the butter. Cover and keep warm.
In a large pot of boiling salted water, cook the pasta until al dente; drain. Add the pasta to the ragù and cook over moderate heat, stirring gently, until simmering. Remove from the heat and stir in the 1/2 cup of cheese and the remaining butter. Season with salt and pepper and serve.
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