Divide the egg yolks and egg whites. Place the whites in your extra clean medium/large bowl, and the yolks in a small/medium bowl.
Add half of the 1/4 cup of sugar to the yolks and set aside.
1/4 cup granulated sugar
With a hand beater, start beating the egg whites.
When egg whites are frothy, add about a third of the remaining sugar.
Beat some more and then add another third, beat, and then the remaining sugar.
Keep beating the egg whites until they form stiff peaks. This means that when you bring your whisks up, the tips of the egg whites do not fold over (see video above). Set aside. Beat the egg yolks and sugar until fluffy and a very pale yellow. This should take 3-5 minutes or so. Using a sifter, add the cake flour to the egg yolks.
1/4 cup cake flour
Use the hand mixer to mix until just combined. Add the melted butter and milk, and again, beat until just combined.
1/2 T butter, 1 T milk
Take about one quarter of the egg whites and fold into the egg yolks with a spatula to "lighten" the batter.
Once mixed in, pour the yolks into the whites, and gently fold the batter to combine. I like to run my spatula around the edge of the bowl and bring the batter up and over into the middle, and then run my spatula through the middle and fold up and over. Make sure you get the bottom mixed in as well, as it can be easy to forget to lift up and over from the bottom. Make sure you don't overmix, or this will deflate the batter and your cake won't be fluffy. Think "light" touch. Tip: Even if there are still little pockets of whites that aren't fully mixed in, the only person who will notice will be you. So it's okay. Pour the batter into the springform pan. If you are scraping the remaining batter into the pan, make sure not to plop it in the middle, but try to pour it to the sides. This will help keep the middle from sinking. Optional: lift the pan up a few inches and drop, on the tabletop, to help bring some of the air bubbles up. I sometimes do this and I sometimes don't, and honestly I don't know if it makes a difference, but some recipes I've seen swear you need to.
Bake in the preheated oven on a middle rack for about 25 minutes or until a skewer comes out clean.
Remove from oven and place on a wire rack.
Remove the springform, and peel away the parchment on the sides.
Place the cake top side down, and peel away the remaining parchment paper lining the bottom.
Allow to cool.