Put the pineapple into a blender or food processor and blitz to a pure. To make the stock syrup, put all the ingredients in a large pot with 500ml water, slowly bring to the boil and stir until the sugar has dissolved, then remove from the heat.
Tip the pineapple pure and the lime juice into the syrup and stir well. Leave to cool, then strain and churn in an ice-cream maker following manufacturers instructions.
Place in a container and freeze. Alternatively, tip the syrup into a large tray and freeze until it starts to set, then every hour or so break up the ice with a fork.
Serve the sorbet scooped into dessert glasses with a few slices of mango.