To Make the Cake
Sift together the flour, baking powder and salt. Whisk together the milk and egg whites in a medium bowl.

Put the sugar and lemon zest in a mixer bowl or another large bowl and rub them together with your fingers until the sugar is moist and fragrant.Add the butter and working with the paddle or whisk attachment, or with a hand mixer, beat at medium speed for a full 3 minutes, until the butter and sugar are very light.

To Make the Buttercream

Put the sugar and egg whites in a mixer bowl or another large heatproof bowl, fit the bowl over a plan of simmering water and whisk constantly, keeping the mixture over the heat, until it feels hot to the touch, about 3 minutes.The sugar should be dissolved, and the mixture will look like shiny marshmallow cream.Remove the bowl from the heat.Working with the whisk attachment or with a hand mixer, beat the meringue on medium speed until it is cool, about 5 minutes.Switch to the paddle attachment if you have one, and add the butter a stick at a time, beating until smooth.Once all the butter is in, beat in the buttercream on medium-high speed until it is thick and very smooth, 6-10 minutes.During this time the buttercream may curdle or separate – just keep beating and it will come together again.On medium speed, gradually beat in the lemon juice, waiting until each addition is absorbed before adding more, and then the vanilla.You should have a shiny smooth, velvety, pristine white buttercream. Press a piece of plastic against the surface of the buttercream and set aside briefly.

To Assemble the Cake

Using a sharp serrated knife and a gentle sawing motion, slice each layer horizontally in half. Put one layer cut side up on a cardboard cake round or a cake plate protected by strips of wax or parchment paper.Spread it with one third of the preserves.Cover the jam evenly with about one quarter of the buttercream.Top with another layer, spread with preserves and butter cream and then do the same with a third layer (you’ll have used all the jam and have buttercream leftover).Place the last layer cut side down on top of the cake and use the remaining buttercream to frost the sides and top. Press the coconut into the frosting, patting it gently all over the sides and top.

Serving

The cake is ready to serve as soon as it is assembled, but I think it’s best to let it sit and set for a couple of hours in a cool room – not the refrigerator. Whether you wait or slice and enjoy it immediately, the cake should be served at room temperature; it loses all its subtlety when it’s cold. Depending on your audience you can serve the cake with just about anything from milk to sweet or bubbly wine.

Storing
The cake is best the day it is made, but you can refrigerate it, well covered, for up to two days. Bring it to room temperature before serving. If you want to freeze the cake, slide it into the freezer to set, then wrap it really well – it will keep for up to 2 months in the freezer; defrost it, still wrapped overnight in the refrigerator.

Playing Around
Since lemon is such a friendly flavour, feel free to make changes in the preserves: other red preserves – cherry or strawberry – look especially nice, but you can even use plum or blueberry jam.