Make sauce: In a bowl whisk sugar and yolks to blend. Add coconut milk and pineapple puree and continue to whisk. Pour into a heavy saucepan and heat, stirring constantly for about 6 minutes, until custard thickens and coats back of a spoon. Make sure you don't bring it to a boil. Strain custard through a sieve into a bowl and stir in Jamaican rum. Cool, cover and refrigerate, overnight, if desired.
Make tart: Preheat oven to 325 degrees F. Roll out puff pastry dough, cut out 5 6-inch rounds and transfer to baking sheets. Using a fork, prick dough all over.
In a small bowl whisk icing sugar and egg yolk to blend and brush over dough rounds. Bake 15 minutes until golden brown. Cool.
Heat a heavy, large non-stick skillet over high heat, add pineapple and cook until golden brown, about 1 minute per side. Preheat grill or broiler.
Arrange pineapple wedges on each pastry round, covering them completely.
Sprinkle each tart with 1 tablespoon sugar. Watching carefully, grill or broil until edges of pineapple begin to brown, for about 5 minutes.
To serve, transfer tarts to large plates, spoon sauce around and garnish with mint sprigs.