To make the ice cream, place the milk, cream and ground cardamom in a saucepan. Bring to the boil and then set aside for at least an hour to infuse. Whisk the egg yolks, sugar and salt together in a bowl.
Bring the milk mixture back to a slow bubble then pour over the egg mixture, whisking constantly. When smooth, pour through a sieve back into the saucepan and cook over a fairly low heat until the mixture coats the back of a spoon. Leave to cool down and then churn in an ice-cream machine according to manufacturer’s instructions.
To make the cake, preheat the oven to 180C/160C Fan/Gas 4 and line a 20x26cm/8×10½in roasting tin with baking paper. Whisk the yoghurt, coconut oil and sugar together until smooth, then beat in the eggs one at a time. Gently fold in the desiccated coconut, flour and baking powder, taking care not to overmix. Spoon the mixture into the tin.
Scatter the mango all over the cake mixture – do not worry if it looks like a bit too much as the cake will rise up around it. Transfer to the oven and bake for 30–35 minutes, until firm to the touch and a skewer inserted into a non-mango bit comes out clean.
Leave the cake in the tin for 5 minutes, then gently lift it out onto a wire rack. Leave to cool briefly before scattering over the coconut flakes.
Serve the cake in slices, warm or at room temperature, with the ice cream.
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