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1
Halve leeks lengthwise, then coarsely chop. Wash leeks in a bowl of cold water, agitating them, then lift out onto paper towels and pat dry.
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2
Cook bacon in a 4-quart heavy pot over moderate heat, turning occasionally, until crisp, 6 to 8 minutes. Transfer to paper towels.
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3
Pour off all but 2 teaspoons fat from pot, then add oil and cook leeks over moderate heat, stirring occasionally, until softened, about 6 minutes. Add celery root and cook, stirring, 2 minutes. Add water and broth and bring to a boil, then reduce heat and simmer, uncovered, until celery root is very tender, 35 to 40 minutes.
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4
While soup simmers, thinly slice apple lengthwise into 1/8-inch-thick slices with slicer, working around core, then cut slices into 1/8-inch matchsticks with a knife. Gently toss with celery and celery leaves.
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5
Puree soup in batches in a blender until smooth (use caution when blending hot liquids), transferring to a bowl. Return soup to cleaned pot. (If soup is too thick, thin with 1/2 to 3/4 cup water.) Stir in salt, pepper, and half-and-half and cook over moderately low heat, stirring occasionally, until warm. Season with salt, then divide among 4 bowls and top with apple-celery mixture and coarsely crumbled bacon.
