Preheat the oven to 325°F.: The oven should be fully heated before you place the pan inside, which ensures even rising and steady baking. You will notice a gentle, warm aroma fill the kitchen as it comes up to temperature, and the oven light will help you watch the cake without opening the door. A common mistake is placing the cake in too cool an oven, which causes poor rise and dense texture. If your oven runs hot or cool, use an oven thermometer to verify accuracy.
Sift the cake flour, sugar, baking powder, and salt into a large mixing bowl. Make a well in the center, and add the oil, egg yolks, cold water, vanilla, and orange extract. Mix until smooth.: As the dry mixture sifts, the air incorporated creates a lighter base for the batter, and the combined dry ingredients will smell faintly of sweet flour and citrus from the extracts. Mixing the well ingredients in the center gives an emulsion where the oil and yolks disperse evenly, preventing streaks of fat. If you overmix after combining, gluten develops and the cake loses tenderness, so stop as soon as the batter looks homogeneous. Scrape the bowl sides to ensure nothing is clinging and to guarantee even texture.
In another large mixing bowl or the bowl of a stand mixer, beat the egg whites and cream of tartar together until they form stiff peaks. Pour the batter mixture into the egg whites, folding it in gently so the egg whites don’t deflate.: When you beat the egg whites with cream of tartar , you will see them transition from frothy to glossy peaks that stand tall. The sound changes too, from a rapid splashing to a thicker, almost muffled beat. Folding requires a light hand, using a spatula in a wide arc to preserve the trapped air, which produces the cake's signature lift. If you stir aggressively, the volume will collapse, yielding a denser cake. To test, lift the spatula and watch for ribbons that slowly sink back into the batter.
Pour the batter into an ungreased 10-inch angel food tube pan, and spread evenly. Bake for 55 minutes, then increase the heat to 350°F and bake an additional 10-15 minutes, until the cake is golden brown on top and a toothpick inserted in the center comes out clean. Remove from the oven and let cool upside down. Allow to cool completely, then release from the pan by running a plastic knife around the edges of the pan. Invert onto a serving platter.: As the batter bakes, the oven will fill with a toasty, sweet aroma and you should see the cake climb and dome slightly before settling into an even top. The dual temperature step allows gentle initial rise, then a final blast to set the exterior and encourage a golden finish. Cooling upside down prevents collapse by using gravity to keep the center elevated; you will hear a faint settling sound as steam escapes. A common error is greasing the pan which prevents the cake from clinging to the sides while cooling and causes it to fall; always use an ungreased tube pan for chiffon cakes. When releasing from the pan, slide a narrow tool carefully to avoid tearing the delicate crumb.
When the cake has cooled, make the frosting by adding the butter to a large mixing bowl or the bowl of a stand mixer. Beat until light and fluffy. Add the orange juice, orange zest, vanilla, and powdered sugar, and mix until combined. Increase the speed to high and beat until light and fluffy.: The frosting should smell bright and citrusy as the orange zest and orange juice are incorporated. As you beat the softened butter with the sugar, the mixture becomes pale and silky, transforming into a spreadable cloud. Beating at low speed first prevents powdered sugar from puffing into the air, then raising the speed gives the frosting a whipped, airy quality. If the frosting becomes too loose, chilling it briefly firms it up; if it is too stiff, add a teaspoon of juice at a time to loosen. Avoid overheating the butter, which yields greasy frosting.
Spread the frosting over the cooled cake and decorate it with fresh fruit, if desired.: The final assembly is tactile and visual, as the smooth frosting glides over the tall, spongy cake creating soft peaks where your spatula lifts away. Fresh fruit adds bright color and a juicy contrast that cuts through sweetness, and placing fruits strategically creates an inviting presentation. If you apply frosting while the cake is still warm, it will melt and slide, so patience is essential. For clean slices, chill the frosted cake briefly so the frosting firms, and use a sharp knife wiped between cuts.