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Finely chop 1 garlic clove. In a medium skillet, heat 1/4 cup olive oil over medium heat. Add chopped garlic and cook, stirring, until fragrant, about 30 seconds. Add breadcrumbs and cook, stirring, until golden brown, about 5 minutes; set aside.
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Bring a large pot of water to a boil over high heat. Generously salt boiling water and add pasta. Cook until still very firm, 5 to 6 minutes. Drain, reserving 1 cup pasta water.
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Meanwhile, in a large high-sided skillet, heat remaining 1/4 cup oil over medium-high heat. Crush remaining 4 garlic cloves and add to skillet along with capers, and raisins; cook, stirring, for 1 minute. Add chicken stock, preserved lemon, lemon juice, butter, Aleppo pepper, and a pinch of salt.
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Bring to a simmer and add pasta. Cook, stirring often, until the pasta is al dente, about 3 minutes; remove from heat. Remove garlic cloves and discard. Stir in pine nuts, parsley, grated Parmesan and bottarga. Add reserved pasta water, 1/4 cup at a time, if pasta seems too dry.
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Garnish with reserved breadcrumb mixture, shaved parmesan and bottarga, and drizzle with extra virgin olive oil. Serve immediately.