Preheat the oven to 325° F.
Separate the egg yolks and the egg whites. You will need 6 yolks and 7 egg whites.
In a stand mixer, combine the flour, sugar, baking powder, and orange zest.
Make a well in the middle and add in the 6 egg yolks, vegetable oil, orange juice, and vanilla extract. Mix on medium until combined.
Put the egg whites in a separate mixing bowl. You can add the optional cream of tartar to it, which can help form stiff peaks. Turn the mixer to medium speed and beat until soft peaks form, then beat on high until stiff peaks form. You've hit stiff peak egg whites when you have glossy peaks that stand straight.
With a large rubber spatula or wire whisk, gently fold the egg whites (in three additions) into the egg yolk batter just until blended (being careful not to deflate the egg whites).
Combine thoroughly, making sure there aren't any white streaks in the batter.
Pour the batter into an ungreased tube pan (a 10-inch chiffon or angel cake pan).
Bake for 55 to 60 minutes.
To make the glaze, combine the orange juice, sugar and cornstarch in a saucepan over medium heat. Cook, stirring constantly, for 3 minutes. Remove from heat and cool completely before using.
When a toothpick is inserted and comes out clean, remove the pan from the oven. It will be spongy to the touch.
Immediately turn the pan over onto a cooling rack with the cake still in it.
Allow it to cool completely, then use a knife around the edges of the pan to free the cake.
Serve with fresh orange slices and whipped cream, if desired.