Preheat oven to 350F (175C). Line a 9x13 inch baking pan with parchment paper.
Whisk egg yolks, 1/2 cup sugar, vanilla, and salt until pale and slightly thickened, about 2 minutes. Whisk in the milk.
Sift in the flour, cornstarch, and baking powder. Fold gently until just combined. Do not overmix.
In a clean dry bowl, whisk egg whites with cream of tartar on medium speed until foamy. Gradually add the remaining 1/4 cup sugar and whisk to stiff, glossy peaks.
Fold one-third of the meringue into the yolk mixture to loosen it. Add the remaining meringue in two additions, folding very gently to preserve the air.
Transfer to the prepared pan and bake for 14-16 minutes, until a toothpick comes out with moist crumbs. The cake will be pale in color - this is normal for a chiffon sponge.
Let cool completely in the pan.