Peel and core the pineapple and cut into 8 slices. Place on the barbecue or griddle pan for 2-3 minutes each side, until charred. Keep warm.
Meanwhile, put the sugar, butter and double cream in a small saucepan. Sit the pan on the barbecue or a low heat on the hob and stir until the sugar has dissolved. Allow to simmer for 2 minutes, then stir in the rum.
Arrange two slices of pineapple on each serving plate and spoon over the sauce. Scatter over the mint leaves to serve.