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1
Adjust oven rack to upper-middle position and preheat oven to 400°F. Line rimmed baking sheet with foil. Place bread on sheet cut side up.
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2
In small saucepan over medium heat, melt butter with garlic. Cook until garlic is fragrant and has softened slightly, about 4 minutes. Spoon garlic butter over bread and season with salt. Sprinkle with Parmesan. Set aside.
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3
Bring a large pot of salted water to a boil over high heat. In large skillet over medium heat, melt butter. Add shallots and cook, stirring, until softened and just beginning to brown, about 8 minutes. Stir in garlic and cook until fragrant, about 30 seconds.
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4
Transfer shallot mixture to blender. Add tomatoes (with juice) and tomato paste. Blend until smooth.
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5
Transfer tomato mixture back to skillet and stir in chili flakes, vodka, 1 1/2 teaspoons salt, and sugar. Bring to boil over medium heat. Reduce heat to medium-low and simmer, stirring occasionally, until slightly thickened and flavors are melded, about 15 minutes. Stir in cream and season to taste. Stir in chicken and cook until just cooked through, about 2 minutes. Keep warm while pasta cooks.
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6
Cook pasta according to package directions. Meanwhile, place garlic bread in oven and bake until cheese is starting to brown, about 10 minutes. Remove from oven and sprinkle with parsley. Drain cooked pasta, reserving 1 cup of pasta water. Toss pasta with sauce, adding pasta water as necessary until sauce reaches desired consistency. Season to taste with salt and pepper if necessary. Stir in basil. Serve pasta and bread immediately, passing additional cheese tableside if desired.
