For the pineapple-mint sauce
Peel and core the pineapple and cut into pieces. Place the pineapple in a saucepan with the coconut milk, the sugar, and the rum. Bring to a simmer, cover and cook over low heat until the pineapple is completely soft. Remove from the heat, and cool thoroughly. Transfer the pineapple mixture to a food processor, add the mint leaves and puree. Strain through a fine-mesh sieve. Stir in the lime and lemon juices, blending thoroughly. The amount of sugar needed depends on the ripeness of the pineapple; therefore, you will have to make adjustments accordingly.