For the Cake:
Preheat your oven to 350°F (175°C). Grease and flour two 8-inch round cake pans.
In a stand mixer fitted with a whisk attachment, beat the egg whites until stiff peaks form. This should take about 1-2 minutes. Set the egg whites aside in the refrigerator.
Using the same mixing bowl, cream the softened butter for about 2 minutes until pale and fluffy.
Add the sugar to the butter and beat until the mixture becomes light and fluffy, about 1-2 minutes.
In a small bowl, combine the cake flour, salt, and baking powder. Set aside.
In another bowl, mix the milk with the almond extract.
Gradually add the dry ingredients to the butter-sugar mixture, alternating with the milk mixture. Start and end with the dry ingredients, mixing gently between additions.
Gently fold the beaten egg whites into the batter, being careful not to overmix to avoid making the cake dense.
Divide the cake batter evenly between the two prepared pans.
Bake for 25-27 minutes, or until the tops of the cakes spring back when lightly touched.
Allow the cakes to cool in the pans for 10 minutes, then turn them out onto a wire rack to cool completely.
For the Frosting:
In a medium saucepan, whisk the flour into the milk over medium-low heat. Stir constantly until the mixture thickens to the consistency of mashed potatoes, about 12-15 minutes.
Remove the pan from the heat and cool the mixture by placing the saucepan in a bowl of ice for 5-10 minutes. The mixture should be at room temperature before moving to the next step. Stir in the almond extract.
If possible, process the granulated sugar in a food processor for about 1 minute to make the granules finer.
In a stand mixer with the whisk attachment, cream the softened butter with the processed sugar until the mixture becomes light and fluffy, about 5 minutes.
Add the cooled flour mixture to the butter-sugar mixture and beat for another 3-5 minutes, until the frosting is light and airy, with a whipped cream-like texture.
To Assemble the Cake:
Once the cakes have cooled completely, place one layer on a cake plate and spread an even layer of frosting on top.
Place the second cake layer on top and use the remaining frosting to cover the top and sides of the cake.
Decorate the sides and top with sliced almonds and whole almonds as desired.