These delicious rum-syrup-soaked yeasted cakes are traditionally made in plain-sided moulds or ring moulds, but look more decorative if you make them in mini kugelhopf tins.
Heat the milk in a small jug in the microwave or in a small pan on the hob until lukewarm. Combine the flour, sugar and salt in the bowl of a stand mixer fitted with the dough hook. Crumble in the yeast, and add the eggs, milk and butter and mix on a medium speed for a few minutes until combined. Scrape down the sides with a rubber spatula and mix for a further 5–7 minutes, or until the dough is silky smooth and elastic. Cover with cling film and leave to rise at room temperature for about 1 hour, until doubled in size.
Meanwhile make the syrup. Put the sugar, star anise, cinnamon sticks, vanilla pod, and orange and lemon rinds in a large pan. Add 1 litre of water, slowly bring to the boil and simmer for 3 minutes. Add the pineapple slices and simmer gently 15 minutes, until the pineapple is tender. Leave to cool for 5 minutes, then, using a slotted spoon, scoop the pineapple from the syrup and set aside. Add the rum to the syrup and leave to cool.
Once the dough has risen, knock it back in the bowl and spoon it into the large piping bag fitted with the 1cm nozzle. Pipe the dough into the kugelhopf moulds, filling each three-quarters full. Cover loosely with oiled cling film and leave to prove for about 30 minutes, until the dough starts to rise above the top of the moulds.
Meanwhile, heat the oven to 180°C/160°C fan/Gas 4.
Once the babas have proved, bake them for 15–20 minutes, until risen and golden brown. Leave to cool in the moulds for 2 minutes, then remove and submerge the babas, two at a time, into the rum syrup, soaking them for about 8 seconds on both sides. Leave on a wire rack to cool.
To make the mascarpone cream, whip the cream with the mascarpone, icing sugar and vanilla until it will hold soft peaks. Place the mixture in the large piping bag fitted with the small decorative nozzle and chill until needed.
Peel and dice the kiwi fruit, dice the cooked pineapple and scoop the pulp from the passionfruit, and set it all aside.
Make the glaze. Warm the apricot jam with the lemon juice and 2 tablespoons of the rum syrup in a small pan or the microwave, and stir to combine. Pass the mixture through a sieve and then brush this over the babas.
Pipe the top of each baba with whipped cream and decorate with the diced pineapple and kiwi and the passionfruit pulp and finish with the lime zest and a mint leaf. Serve with rum-syrup-filled mini disposable pipettes.