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1
Preheat oven to 450u00b0F with rack in middle.
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2
Wrap beets in foil and roast until tender, about 1 1/2 hours. Let stand until cool enough to handle, then slice crosswise into 1/4-inch-thick rounds. Cool completely.
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3
Meanwhile, finely grate ginger with a Microplane over a kitchen-towel-lined bowl. Carefully gather towel around ginger and squeeze until you have 2 tablespoons ginger juice. Whisk in orange juice, sugar, and oil. Season with salt and pepper. Divide vinaigrette evenly between 2 small bowls.
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4
Cut pears lengthwise around core into 1/4-inch-thick slices. Cut out 18 rounds from slices using cookie cutter and put in one bowl of vinaigrette.
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5
Cut out 18 rounds from beet slices and put in other bowl. Toss pears and beets with vinaigrette to coat well.
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6
To assemble napoleons, put 1 beet round on each of 6 plates (see cooks' note, below) and top with a tarragon leaf. Top with 1 pear round, then another tarragon leaf. Repeat layering 2 more times. Discard vinaigrette used for beets.
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7
Toss greens with some of remaining vinaigrette and place around each napoleon. Finely grate apple (including skin) into a bowl. Spoon a heaping teaspoon apple on top of each napoleon, then sprinkle with sea salt and poppy seeds. Drizzle with more vinaigrette if desired.
