In a large bowl, mix flour, baking powder, salt, and 1-1/4 cup sugar. Set aside.
In a medium bowl, whisk egg yolks, oil, milk, and vanilla. Add to dry ingredients and combine until smooth. Set aside.
In a medium bowl, beat egg whites and cream of tartar until frothy. Add remaining sugar and whip until stiff peaks form.
Gently mix about 1/3 egg white mixture into cake batter. Fold in remaining egg white mixture, keeping it airy.
Grease, flour, and add a parchment layer to cake pans. Add a heaping 3/4 cup of batter to each pan, spreading evenly. Don't forget the edges.
Bake at 375° for about 10 minutes, or until slightly golden. Cool on racks, clean pans, and repeat until you have 7 layers.