Put the water, sugar, star anise, cinnamon and lemon zest into a saucepan and bring slowly to the boil, stirring occasionally.
Simmer for 10 minutes, or until the sugar syrup is quite clear.
Set aside to cool completely, then place in the fridge for an hour or two, or until cold.
Top and tail the guavas, but do not peel.
Cut into chunks and place in a liquidizer, or a food processor fitted with a metal blade.
Whizz to a rough purée.
Tip the purée into a sieve set over a large bowl and, using the back of a soup ladle to press vigorously down on the pulp, strain off the liquid.
Discard the pulp and seeds.
Strain the chilled sugar syrup into the bowl containing the strained guava (discard the spices and lemon peel).
Add the lemon juice and cream (or yoghurt), and stir well to combine.
Place the mixture in the bowl of an ice cream machine and churn until done (or use the freeze-and-beat method).
Serve the ice cream in chilled glasses (place them in the freezer an hour before you serve the dessert).
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