Heat the oven to 180C/160C fan/gas 4. Butter and line two loose-bottomed 20cm round cake tins.

Put the butter and sugar in a large mixing bowl. Beat for 5 mins with an electric whisk until pale and fluffy. Whisk in the eggs one at a time, then fold through the flour, grated lime zest and yogurt. Divide the batter between the prepared tins and bake in the centre of the oven for 25-30 mins, or until a skewer inserted in the middle comes out clean. Leave in the tins for a min, then turn out onto wire racks.

To make the syrup, put half the lime juice and all the sugar and mint leaves into a saucepan and bring to a simmer, adding 1 tbsp water if needed to dissolve the sugar. Gently bubble for 7-10 mins, or until syrupy. Remove from the heat and stir through the rum and remaining lime juice. Leave to infuse for 10 mins, then strain into a bowl.

Prick the warm cakes all over with a cocktail stick and pour over the syrup. Leave to cool completely.

To make the buttercream, put the butter, icing sugar and lime zest in a bowl and beat with an electric whisk for 5 mins until light and fluffy. Beat in the cream cheese until just combined, being careful not to overbeat.

Put one of the syrup-soaked sponges on a large serving plate and spoon over one-third of the buttercream, spreading it over with a palette knife. Top with the other sponge and spread the remaining icing over the top and sides of the cake. Decorate with the lime wedges, lime zest and mint leaves. Will keep in the fridge for up to three days.