Preheat your oven to 325°F (160°C). Ensure your oven rack is in the center. Prepare a chiffon cake pan, ungreased.
In a large bowl, whisk together the cake flour, 1 cup of the granulated sugar, baking powder, and salt.
In a separate large bowl, whisk together the vegetable oil, egg yolks, cold water, and vanilla extract until smooth.
Gradually add the wet ingredients to the dry ingredients. Mix on low speed or whisk gently until just combined.
In a clean, grease-free bowl, beat the egg whites until foamy. Add cream of tartar and continue beating, gradually adding the remaining ½ cup of sugar, until stiff, glossy peaks form.
Gently fold about one-third of the beaten egg whites into the yolk batter to lighten it.
Gently fold in the remaining egg whites in two additions until just combined. Be careful not to deflate the egg whites.
Pour the batter into the ungreased chiffon cake pan, not more than ¾ full.
Bake in the preheated oven for 50-60 minutes, or until a toothpick inserted into the center comes out clean.
Immediately invert the pan and cool completely upside down for at least one to two hours.
Once cooled, run a thin knife or spatula around the edges to loosen the cake. Release and invert onto a serving plate.