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1
Spread 1 cup sugar in an even layer in a 10 inch heavy skillet. Arrange apples, cut sides down, on sugar, then cover and cook over low heat, stirring sugar occasionally to ensure that it liquefies evenly (without caramelizing) and turning apples once (to other cut side), until apples are soft, 30 to 40 minutes. Transfer apples with a slotted spoon to a plate to cool. Add anise to syrup in skillet and simmer 2 minutes, then transfer syrup to a bowl and cool to room temp. Discard anise.
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2
Put oven rack in middle position and preheat oven to 375 F. Line a large baking sheet with parchment.
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3
When apples are cool enough to handle, gently remove flesh from apple skins with a melon-ball cutter or thin edge sppon, leaving skins intact. Put apple flesh in a bowl with butter and mash with fork until pureed. Chill until cold, about 1 hour.
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4
Put apple skins on lined baking sheet, then sprinkle both sides of skins with remaining 2 teaspoons sugar. Bake until almost crisp and just caramelized, 7 to 10 minutes. Transfer skins on sheet to a rack to cool. (Skins will continue to crisp as they cool.)
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5
Using 2 spoons, form a quenelle (egg-shaped mound) of chilled puree on each of 4 plates. Drizzle plates with syrup, then top with crisp apple skin.
