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1
Set a 2-quart container and 6 parfait glasses in the freezer.
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2
In a medium bowl, stir together the pineapple juice and cream of coconut.
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3
Working in 2 batches, freeze the mixture in an ice cream machine according to the manufacturer's instructions.
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4
Transfer the sorbet to the chilled container, cover tightly and freeze.
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5
Using a long sharp knife, remove the skin from the pineapple.
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6
Cut the pineapple in half lengthwise and remove the core.
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7
Cut one pineapple half into 1/4-inch dice.
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8
Cut three 1/3-inch thick crosswise slices from the other pineapple half, then cut 2 neat triangles from each slice.
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9
Reserve the remaining pineapple for another use.
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10
In a large, heavy, nonreactive skillet, combine the brown sugar and butter with 1 tablespoon of water and stir over moderately high heat until bubbling.
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11
Add the 6 pineapple triangles and cook until golden brown, 3 to 4 minutes per side.
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12
Transfer the triangles to a plate to cool.
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13
Add the diced pineapple to the skillet and cook until the juices evaporate, about 5 minutes.
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14
Transfer to a bowl and let cool.
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15
Place a scoop of slightly softened sorbet in each of the 6 chilled parfait glasses.
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16
Cover the sorbet with half of the diced pineapple.
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17
Make a second layer with another scoop of sorbet and the remaining diced pineapple.
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18
Top the parfaits with the remaining sorbet.
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19
Just before serving, garnish each parfait with a caramelized pineapple triangle and a Coconut Tuiles.
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20
Pass the remaining Coconut Tuiles separately.
