1 For the sponge: Preheat the oven to 190 degrees (fan 175), or gas mark 5, and line a 20x20cm square tin with parchment paper.

2 Put the butter and milk in a small saucepan with the lime zest. Heat to a simmer, and once the butter is completely melted, remove from the heat and set aside.

3 Put the eggs and sugar in a large bowl and whisk together using an electric beater or stand mixer for about five minutes, until doubled in size, pale and thick. Test for readiness by lifting the whisk up and drawing a figure of eight with the batter; if it holds its shape, it is ready. Alternatively, you can do this by hand, but it will take a few minutes longer.

4 In another bowl, sift together the flour, salt and baking powder. In thirds, gently fold the dry ingredients into the egg mix. Add the milk, and fold through until just combined.

5 Pour the mix into the prepared tin and smooth the top.

6 Bake for 20-25 minutes, or until a skewer inserted into the centre comes out clean.

7 Remove from the oven and set aside to cool in the tin slightly while making the coconut-milk soak.

8 Put the coconut milk and sugar in a small saucepan and heat gently until the sugar has dissolved. Remove from the heat and add the coconut rum if using. Cool slightly until warm to touch.

9 Using a skewer, poke holes all over the sponge. Pour the coconut milk over the sponge and allow to soak and cool completely.

10 For the icing, cream the butter and icing sugar together until pale and fluffy. Add the vanilla, followed by the cream cheese, beating until well combined. The frosting should be smooth, thick and creamy, so take care not to overmix, as the cream cheese can get runny if overmixed.

11 To assemble: Turn the coconut cake out onto a serving board. Spread the cream-cheese icing over the sponge and sprinkle the coconut flakes or desiccated coconut on top. Slice into squares to serve.