Add the sugar to a food processor and blend until the sugar is super fine, about 1 minute. Reserve half (about 3/4 cup) of the sugar and set aside.
Add the cake flour, the remaining sugar (about 3/4 cup), and the salt to a medium bowl. Sift into another medium bowl. Sift the mixture back into the original bowl. This helps get rid of any lumps and creates a very fluffy light texture in the cake.
In a large bowl, add the orange zest, cream of tartar and egg whites. Slice the vanilla bean in half, scrape the seeds out with a knife, and add the seeds to the bowl with the egg whites. Using a hand mixer, begin to beat the egg white mixture on medium-high speed. While mixing, slowly stream in the remaining sugar. Beat the mixture until it holds medium peaks, this could take up to 10 minutes.
Set the mixer aside and sift a light dusting of the flour mixture on top of the egg white mixture. Use a rubber spatula to fold the flour into the egg white mixture, this is done by slicing through the middle of the mixture and folding up and over along the side of the bowl to incorporate the flour. Keep sifting and folding until all the flour mixture has been incorporated.
Carefully spoon the mixture into an ungreased 10-inch tube pan. Use a knife to swirl around the pan 2 times to release any unwanted air bubbles. Bake until a toothpick inserted into the cake comes out clean, about 30 minutes.
Remove from the oven and cool upside down on a cooling rack. Let cool for at least 1 hour before removing the cake from the pan and cooling completely.