Step 1

Preheat oven to 180C. Butter two 23cm-diameter cake tins, then dust with flour and line bases with baking paper. Whisk eggwhite, 120ml coconut milk, coconut essence and vanilla in a bowl and set aside. Beat butter and remaining coconut milk in an electric mixer until combined, then add flour, sugar, baking powder, desiccated coconut and a pinch of salt and mix on low until combined. Beat on high for another minute, scraping down sides of bowl, and add eggwhite mixture in 3 batches. Divide between tins and bake until golden and a skewer inserted comes out clean (35-40 minutes). Cool in tins for 15 minutes, then turn out onto wire racks and cool completely.

Step 2

For berry compote, simmer berries and 60ml water in a small saucepan over low heat, covered, until berries are tender (13-15 minutes). Stir in sugar and lemon juice and simmer uncovered until a light syrup forms (5-7 minutes), Cool to room temperature.

Step 3

For buttercream, stir sugar and 60ml water in a small saucepan over medium heat until sugar dissolves, then bring to the boil and cook without stirring until sugar syrup reaches 115C on a sugar thermometer (6-7 minutes). Meanwhile, whisk eggwhite with cream of tartar in an electric mixer until stiff peaks form (6-8 minutes). Turn the mixer off, add a third of the sugar syrup, then whisk on high speed for 10 seconds. Reduce to medium speed and, while whisking, slowly pour in remaining syrup, whisking until the meringue reaches 35C. Add butter a little at a time, whisking to incorporate each addition before adding more. Whisk in vanilla, coconut essence and a quarter of the berry compote. Store refrigerated in an airtight container for 2 days. Stand at room temperature to soften until spreadable.

Step 4

To assemble, trim the top of each cake to make level, then halve each horizontally. Place one of the bases outside-down on a cake stand, dot with berry compote and spread 2 tbsp of buttercream on top to just over the sides. Repeat layering, using the 2 top layers next, and finish with other base layer, outside up. Spread remaining buttercream over sides and top and press the coconut flakes all over cake. This cake is best eaten on the day of making, but will keep sealed for up to 2 days.