To serve: finely diced pineapple and coarsely torn mintVanilla-lime ice-cream800 mlpouring cream200 mlmilkFinely grated rind and juiceof 2 limes1vanilla bean, split, seeds scraped10egg yolks200 gmraw caster sugarPineapple granita110 gm (½ cup)raw caster sugar700 gm (about ½ large)pineapple, coarsely chopped60 ml (¼ cup)lime juicePine-lime syrup500 gmcoarsely chopped pineapple330 gmraw caster sugar1vanilla bean, split, seeds scraped1 cup (firmly packed)mint60 ml (¼ cup)lime juice
For vanilla-lime ice-cream, bring cream, milk, lime rind, vanilla bean and vanilla seeds to the simmer in a large saucepan over medium heat, remove from heat and set aside to infuse (10 minutes), then return to the simmer. Whisk yolks and sugar in a bowl until thick and pale (4-5 minutes), add cream mixture, whisk to combine, then return to pan. Stir continuously until mixture coats the back of a wooden spoon thickly (5-6 minutes), transfer to a bowl, remove vanilla bean (discard) and refrigerate until chilled. Stir in lime juice, freeze in an ice-cream machine then freeze until required. Makes about 1.5 litres.
For pineapple granita, stir sugar and 125ml water in a saucepan over medium-high heat until sugar dissolves, then bring to the boil, remove from heat and refrigerate until completely chilled. Process pineapple, lime juice and sugar syrup in a food processor until smooth, pass through a coarse sieve (discard solids) into a shallow metal tray and freeze, stirring and scraping occasionally with a fork until crystals form and granita is frozen (3-4 hours). Makes about 1 litre.
For pine-lime syrup, stir pineapple, sugar, vanilla bean and seeds and 250ml water in a saucepan over medium-high heat until sugar dissolves, bring to the boil and cook until pineapple is translucent (8-10 minutes). Remove from heat, stir in mint and lime juice, cool to room temperature, remove vanilla bean (discard), process mixture in a food processor until smooth, pass through a fine sieve (discard solids) and refrigerate until chilled.
Serve vanilla-lime ice-cream with pineapple and mint, topped with pineapple granita and drizzled with pine-lime syrup.