Ingredients

1. 46 ounces pineapple juice, well chilled
2. 2/3 cup sweetened cream of coconut, such as Coco Lopez, at room temperature
3. 1 ripe medium pineapple (about 3 1/2 pounds)
4. 1/2 cup light brown sugar
5. 1 tablespoon unsalted butter
6. Coconut Tuiles

Directions

1. Set a 2-quart container and 6 parfait glasses in the freezer. In a medium bowl, stir together the pineapple juice and cream of coconut. Working in 2 batches, freeze the mixture in an ice cream machine according to the manufacturer's instructions. Transfer the sorbet to the chilled container, cover tightly and freeze.
2. Using a long sharp knife, remove the skin from the pineapple. Cut the pineapple in half lengthwise and remove the core. Cut one pineapple half into 1/4-inch dice. Cut three 1/3-inch thick crosswise slices from the other pineapple half, then cut 2 neat triangles from each slice. Reserve the remaining pineapple for another use. 
3. 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. Add the 6 pineapple triangles and cook until golden brown, 3 to 4 minutes per side. Transfer the triangles to a plate to cool. 
4. Add the diced pineapple to the skillet and cook until the juices evaporate, about 5 minutes. Transfer to a bowl and let cool. (The pineapple can be prepared up to 4 hours ahead.) 
5. Place a scoop of slightly softened sorbet in each of the 6 chilled parfait glasses. Cover the sorbet with half of the diced pineapple. Make a second layer with another scoop of sorbet and the remaining diced pineapple. Top the parfaits with the remaining sorbet. (The parfaits can be assembled up to 30 minutes ahead and held in the freezer.) Just before serving, garnish each parfait with a caramelized pineapple triangle and a Coconut Tuile. Pass the remaining Coconut Tuiles separately. 
6.  

Make Ahead

The pineapple can be prepared up to 4 hours ahead.

Serve With

Coconut Tuiles