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Cook broccoli flowerets in boiling water to cover 1 minute.
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They should be crisp-tender.
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Drain and set aside.
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Heat the olive oil in a medium saucepan; add minced garlic and cook over low heat until garlic is barely colored.
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Remove from heat.
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Cook the pasta in 5 quarts of rapidly boiling water.
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While pasta is cooking put the reserved broccoli in with the garlic and oil and heat through for a minute or 2.
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Drain pasta and place it in a warmed serving dish.
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Add butter; toss well and pour on the broccoli sauce.
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Sprinkle with cheese and toss again.
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Serve immediately with ground pepper to taste.