Preheat oven to 350 degrees F. Grease and flour four 6" round cake pans. Line the bottoms with parchment paper.
Combine cake flour, sugar, baking powder, and salt in a stand mixer fitted with the paddle attachment.
Add the butter and beat until a crumbly mixture forms, just starting to come together.
Add the egg whites one at a time, and beat to combine. Add the egg and beat to combine.
Combine milk and vanilla extract together in a measuring cup. Add to the mixer in three additions, beating well after each addition.
If you want to be precise, weigh the batter so you know how much to put in each pan.
Pour one-fifth of the batter into one of the prepared 6" pans. Repeat with the other 6" pans. You will have one-fifth of the batter left over. You can bake an extra layer or make some cupcakes!
Bake for about 24-28 minutes, rotating halfway. The cakes should be set and a skewer inserted in the center should come out with a few crumbs on it.
Remove and place on wire racks. Run a knife around the edges for easier removal. Let cool for about 20 minutes and then invert pans to remove cakes. Let them finish cooling before decorating.
For the buttercream:
Combine the sugar and egg whites in a medium metal bowl and place over a pan of simmering water.
Whisk the sugar mixture constantly over heat until the sugar is dissolved and the mixture looks smooth and shiny. Continue whisking until the mixture reaches 160 degrees F.
Remove mixture from heat and pour into a stand mixer bowl. Whisk on medium speed for about 5 minutes until the mixture has cooled.
Switch to the paddle attachment and with the speed on low, add the butter a few pieces at a time, beating until smooth. Do not add the butter too quickly or beat too quickly or the buttercream may break.
When all the butter has been added, beat the buttercream on medium-high speed for about 6-10 minutes until it is very thick and smooth. It may appear to separate briefly but continue beating and it should come back together.
Add in the vanilla and almond extracts and beat to combine. Add food coloring as desired.
The buttercream is ready to be used. Place a piece of plastic wrap against the surface until you are ready to use it to prevent it from drying out.
To assemble the cake:
Level off cake layers if necessary. Place one cake layer on a cake board or cake decorating stand.
Spread some of the buttercream over the cake layer evenly. Place a second cake layer on top and spread some more buttercream over the cake layer. Repeat the process with the third layer. Top with the fourth layer.
Spread a crumb coat of buttercream over the top and sides of cake (see here for tips on doing a crumb coat). Refrigerate for about an hour to let the frosting set.
When you are ready to finish the cake, spread the rest of the buttercream over the top and sides of the cake with an offset spatula. Finish decorating as desired.
Recipe by Dessert First at https://dessertfirstgirl.com/2019/03/mermaid-birthday-cake.html