Prep: Preheat oven to 350°F. Line only the bottom of two 6-inch pans.
Yolk batter: Whisk egg yolks then add salt, sugar, milk, oil, pistachio paste, and vanilla until smooth. Sift in cake flour and whisk smooth.
Meringue: Whisk egg whites until foamy. Add sugar 1 tbsp at a time while whisking. Increase speed and whisk to soft peaks.
Fold: Whisk a small amount of meringue into yolk batter to lighten. Fold in remaining meringue in 2 additions with a spatula until just combined.
Bake: Divide between pans. Bake 20-25 minutes until toothpick has just a few moist crumbs. Flip immediately onto wire rack. Cool completely.
Slice: Release from pan with a knife. Slice each layer into ½ inch thick sheets.