Preheat oven to 375 degrees F (190 degrees C). Butter a cake pan (you can also line it with parchment paper if you want) – we used a rectangular one, but round is fine too!
Melt butter and milk together on the stove. Let the mixture cool a bit, until it’s not burning hot but just a bit warm.
Beat eggs and sugar together until light and fluffy and tripled in volume, either in a stand mixer, with a hand mixer, or by hand with a whisk. Add the vanilla extract in right before the eggs and sugar have tripled in volume, just so it’s evenly combined.
Combine flour, baking powder, and salt in a separate bowl.
Now you are going to add your cooled butter/milk mixture and flour mixture into the fluffy egg/sugar mixture. Alternate between adding the two mixtures in two separate stages, making sure to sift the dry mixture in and fold gently with a rubber spatula, so as not to deflate the eggs. You can also use the paddle attachment on the stand mixer on low speed. So: sift in 1/2 of the dry mixture, fold together, add 1/2 of the butter/milk, fold, sift in 1/2 of the dry, fold, then add 1/2 of the butter/milk. Finally, fold everything together a few times at the end, until combined. You should have a smooth cake batter.
Pour into the pan and bake for 20-25 minutes, until the top is golden brown and a cake tester comes out almost completely clean. (note: make sure to continue the recipe as it is baking so you can add the meringue to the top immediately!)
You’re going to add your topping and bake for a bit longer, so you don’t want the cake to be completely done at this stage. Of course, you also don’t want it to be liquid, so just check it with a cake tester, skewer, or knife – a little bit of batter should still stick onto the tester, but not much.
While the cake bakes, make your meringue. In the bowl of a stand mixer with the whisk attachment, add the egg whites and splash of lemon juice. Start whipping until the egg whites look frothy.
Add in the vanilla extract. Slowly add the sugar one tablespoon at a time while the mixer is running. If you add it too quickly, the sugar will not dissolve and it will end up grainy!
Once all the sugar has been added, keep whisking until it has reached stiff peaks – this can take a little while!
Once the meringue is ready, add in the coconut and mix to combine.
When the cake has baked for around 20 minutes, carefully spoon the meringue over the cake and spread it out to cover the whole cake. Do not dump the meringue in one spot or you risk collapsing the cake!
Put it back into the oven and bake for another 10-15 minutes (the meringue will darken a little bit on the top - the goal is to have a meringue that doesn't deflate!)
Let your cake cool, slice, and enjoy!