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1
Bring sugar, water, and star anise to a boil over moderately high heat, stirring until sugar is dissolved, then reduce heat and simmer syrup 5 minutes.
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2
Cool, then discard star anise.
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3
Peel 1 pineapple half, reserving rind, then core and cut into 1-inch chunks.
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4
Squeeze juice from rind with your hands into a blender and add chunks.
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5
Puree at high speed until very smooth, about 1 minute.
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6
Stir puree into syrup and chill, covered, until very cold, about 4 hours.
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7
Freeze in ice cream maker, then transfer to an airtight container and put in freezer to harden, at least 1 hour.
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8
Preheat oven to 500F.
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9
Peel remaining pineapple half but do not core.
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10
Trim ends and cut remainder crosswise into 1/2-inch-thick slices.
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11
Brush some butter on a baking sheet, then arrange pineapple in 1 layer over it and brush with rest of butter.
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12
Roast pineapple slices in middle of oven until undersides are browned (tops will only color slightly), 12 to 15 minutes.
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13
Remove from oven and turn slices over.
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14
Cool on baking sheet on a rack to room temperature.
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15
Arrange 3 slices of roasted pineapple on each of 4 plates and top with sorbet.
