1. Preheat Oven: Set your oven to 350°F (175°C).
2. Prepare Dry Ingredients: In a bowl, combine 3/4 cup of sugar with the sifted cake flour. Sift this mixture three times to ensure it’s well aerated.
3. Whip Egg Whites: In a large, clean bowl, beat the egg whites on medium speed until they become frothy. Add the cream of tartar and salt, then continue beating until soft peaks form.
4. Add Sugar: Gradually add the remaining 3/4 cup of sugar to the egg whites, a tablespoon at a time, beating continuously until stiff, glossy peaks form.
5. Incorporate Dry Ingredients: Gently fold the flour and sugar mixture into the egg whites, a little at a time, using a spatula. Be careful not to deflate the batter. Add the vanilla extract and fold until just combined.
6. Transfer to Pan: Pour the batter into an ungreased 10-inch tube pan. Smooth the top with a spatula to ensure even baking.
7. Bake: Place the pan in the preheated oven and bake for 40-45 minutes, or until the cake is golden brown and springs back when lightly pressed.
8. Cool: Immediately invert the pan onto a cooling rack and let the cake cool completely upside down. This prevents the cake from collapsing. Once cooled, run a knife around the edges to release the cake from the pan.

Fluffy Icing:

1. Combine Ingredients: In a heatproof bowl, combine the egg whites, sugar, water, and corn syrup.
2. Heat Mixture: Place the bowl over a pot of simmering water (double boiler). Using a hand mixer, beat the mixture on low speed until the sugar dissolves and the mixture reaches 160°F (70°C) on a candy thermometer.
3. Whip Icing: Remove the bowl from the heat. Increase the mixer speed to high and beat until stiff, glossy peaks form and the icing has cooled to room temperature. This should take about 5-7 minutes.
4. Add Flavoring: Beat in the vanilla extract until just combined.
5. Frost Cake: Immediately spread the icing over the cooled angel food cake. Use a spatula to create swirls and peaks for a decorative finish.