Preheat oven to 375 degrees F (190 degrees C).
Butter a cake pan and add parchment paper if you would like to for easy removal - we used a rectangular pan (9x13 inches or about 23x33 cm), but a large round pan 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.
Combine flour, baking powder, and salt in a separate bowl.
Beat eggs and sugar together, either in a stand mixer with the whisk attachment, with a hand mixer, or by hand with a whisk.
The eggs and sugar should about double in volume and become light in color and a little bit thicker than liquid. When you lift the whisk out of the mixture, the mixture that flows back into the bowl should sit on the surface for just a second before sinking back in - that's ribbon stage, and it should be ready for the next step!
Add the vanilla extract to the eggs and sugar and mix together.
Now you are going to add your cooled wet ingredients and dry ingredients into the fluffy egg mixture in batches. You can do this by hand or with a paddle/whisk attachment on your stand mixer. First, sift in half of the dry mixture and fold together gently or run the mixer for just 10-15 seconds on low.
Then, add half of the wet mixture and fold together gently, or run the mixer for another 10-15 seconds on low. If you see dry ingredients stuck on the sides of the bowl, make sure to use a spatula to fold it in.
Repeat the process of sifting in the rest of the dry ingredients, mix, then add the rest of the wet ingredients and mix together, either by folding the ingredients together or running the mixer.
Finally, fold everything together a few times at the end until you have a smooth cake batter, making sure nothing is stuck on the sides or the bottom of the stand mixer bowl.
Pour batter into the prepared cake pan.
Bake for an initial 20-25 minutes, until the top is golden and a cake tester comes out clean. The cake should be just baked, since it will go back in the oven for with the topping on it, and we don't want to overbake it! Continue with the steps for the topping below while the cake is baking!
While the cake bakes, make your topping. Combine butter, brown sugar, and a splash of milk in a saucepan and place on the stove over medium heat.
Once the mixture bubbles, give it 1-2 minutes, or until it looks like it has gotten a bit thicker, then remove from the heat.
Add in the coconut flakes.
Mix well, until the flakes are fully coated.
Once the cake is ready, take it out of the oven and increase the oven temperature to 400 degrees F (205 degrees C).
Pour/spoon the topping onto the cake - try to avoid pouring the topping into one spot on the cake as it could collapse the cake!
Spread it evenly and bake the cake for just 5 more minutes. After baking, the topping should be lightly golden brown.
Once it cools a bit, cut a slice and enjoy!