Preheat oven to 350°F/177°C.
Line a 8" by 4" loaf pan with parchment paper.
Sift the cake flour, baking powder and salt into a bowl. Set aside.
In a clean mixer bowl fitted with a whisk attachment, add in the 2 egg whites and whisk until foamy.
Add in the cream of tartar and continue whisking. Gradually add in half of the sugar and whisk until the egg whites form stiff peaks.
Transfer the whipped egg whites from the stand mixer bowl to a large clean bowl. Set aside.
Using the same stand mixer bowl, replace the whisk with the paddle attachment and add in the butter and the remaining sugar.
Cream the butter and sugar until light and fluffy, about 3 minutes.
Lower the mixer speed and pour in 1 egg yolk at a time.
Mix until the egg yolks are incorporated. Add in the vanilla extract.
Pour in ⅓rd of the milk.
With the mixer on low, add in ½ of the cake flour mixture.
Alternate with the remainder of the milk and flour, which will result in a cake batter.
Take about ⅓rd of the egg whites and fold into the cake batter. Continue folding in the egg whites in thirds, until incorporated. (Don't over mix).
Transfer the batter to the prepared loaf pan and tap a few times to release any trapped bubbles.
Smooth the top with an offset spatula and place into the oven.
Bake at 350°F/177°C for 15 minutes, and then reduce the temperature to 325°F/163°C for another 18-20 minutes, or until a toothpick inserted comes out clean or with the slightest crumbs clinging on.
Let the cake cool completely on a cooling rack before slicing off the ends and cutting the cake into 8 equal square cubes.